UNIVERSITY  OF  CALIFORNIA 
AT   LOS  ANGELES 


GIFT  OF 

'ARNEGIE  INSTITUTION 
OF    WASHINGTON 


Electrochemical   Investigation  of    Liquid 

Amalgams  of  Thallium,  Indium, 

Tin,  Zinc,  Cadmium,  Lead, 

Copper,  and  Lithium. 


THEODORE   WILLIAM   RICHARDS 


WITH  THE  COLLABORATION   OF 

J.  HUNT  WILSON  AND  R.  N.  GARROD-THOMAS. 


PIBLISHED  BY  THE 
CARNEGIE  INSTITUTION  OF  WASHINGTON 

1909 


7  43 


Electrochemical   Investigation  of   Liquid 

Amalgams  of  Thallium,  Indium, 

Tin,  Zinc,  Cadmium,  Lead, 

Copper,  and  Lithium. 


BY 

THEODORE  WILLIAM  RICHARDS 

WITH  THE  COLLABORATION  OF 

J.  HUNT  WILSON  AND  R.  N.  GARROD-THOMAS. 


PUBLISHED  BY  THE 
CARNEGIE  INSTITUTION  OF  WASHINGTON 

1909 


CARNEGIE  INSTITUTION  OF  WASHINGTON 
PUBLICATION  No.  118 


CONTRIBUTIONS  FROM  THE  CHEMICAL  LABORATORY 
OF  HARVARD  COLLEGE 


£ort  (gafttmore  (prcee 

BALTIMORE,  MD.,  U.  S.  A. 


Library 


CONTENTS. 


ELECTROCHEMICAL  INVESTIGATION  OF  LIQUID  AMALGAMS  OF  THALLIUM,  INDIUM,  AND 
TIN.      BY  T.  W.  RICHARDS  AND  J.  H.  WILSON. 

PAGE 

Introduction    I 

Values   of   Constants 3 

Preparation  of  the  Amalgams 8 

Densities  of  the  Amalgams 12 

The   Cell    IS 

The   Potentiometer    17 

Electromotive  Force  between  Thallium  Amalgams 20 

Electromotive  Force  between  Indium  Amalgams 25 

Electromotive  Force  between  Tin  Amalgams 27 

Temperature  Coefficient  of  the  Amalgam  Cells 30 

Application  of  the  Equation  of  Cady 31 

Application  of  the  Equation  of  Helmholtz 33 

Summary     37 

II. 

ELECTROCHEMICAL  INVESTIGATION  OF  LIQUID  AMALGAMS  OF  ZINC,  CADMIUM,  LEAD, 
COPPER,  AND  LITHIUM.    BY  T.  W.  RICHARDS  AND  R.  N.  GARROD-THOMAS. 

Introduction    39 

Zinc  Amalgams   39 

Electromotive  Force  between  Zinc  Amalgams 41 

Determination    of    the    Temperature    Coefficients    of    Cells    containing    Zinc 

Amalgams    43 

Lead    Amalgams    47 

Copper   Amalgam    50 

Iron  Amalgam   54 

Lithium    Amalgams    55 

Application  of  the  Equation  of  Cady 57 

Equation  of  Helmholtz   64 

Comparison  of  Deviations  from  Concentration  Law 68 

Summary    71 


iii 

209154 


I. 

Electrochemical  Investigation  of  Liquid  Amalgams  of 
Thallium,  Indium,  and  Tin. 


BY  THEODORE  W.  RICHARDS  AND  J.  HUNT  WILSON. 


INTRODUCTION. 

The  change  in  free  energy  during  a  chemical  reaction  may  be  regarded 
as  composed  of  at  least  two  separate  quantities,  one  which  may  be  said  to 
be  due  to  the  affinities  involved  in  the  reaction,  the  other  depending  upon 
the  relative  concentration  of  initial  substances  and  products.  The  calcula- 
tion of  the  magnitudes  of  these  quantities  is  a  matter  of  prime  importance, 
for  free  energy  is  the  driving  agency  of  all  earthly  things.  Unfortunately 
the  actual  determination  of  changes  of  free  energy  is  only  possible  in  the 
case  of  easily  reversible  reactions,  and  these  form  a  comparatively  small 
part  of  many  examples  of  chemical  change. 

Of  great  theoretical  importance  in  this  connection  are  the  reversible 
galvanic  cells,  which  involve  in  their  action  simply  the  dilution  of  liquid 
amalgams,  and  consequently  suffer  no  appreciable  change  of  heat  capacity. 
The  study  of  such  cells  can  furnish  much  light  upon  the  second  of  the  two 
independent  quantities  which  together  constitute  the  total  free  energy  of 
a  reaction,  namely,  concentration  effect.  Von  Turin  pointed  out  the 
analogy  between  such  cells  and  the  concentration  elements  first  investi- 
gated by  Helmholtz  and  offered  the  first  consistent  theory  of  amalgam 
cells.  G.  Meyer  measured  cells  of  this  type,  but  much  more  accurate  data 
have  been  obtained  at  Harvard  University.  The  object  of  this  recent  work, 
which  concerned  itself  with  cells  containing  zinc  and  cadmium  amalgams 
over  a  considerable  range  of  concentration,  was  to  test  the  application  of 
the  gas  law  to  solutions  of  this  type,  as  well  as  to  apply  the  equations  of 
Helmholtz  and  of  Cady  to  the  data.  Great  accuracy  was  sought.  Since 
the  two  metals  presented  widely  different  phenomena,  and  since  both  of 
these  metals  are  bivalent,  it  seemed  desirable  to  extend  the  work  by  meas- 
uring similar  cells,  employing  a  wide  variety  of  other  metals  with  other 
valencies.  In  this  way  a  more  complete  survey  of  the  possibilities  would 
certainly  be  obtained. 


2  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

This  monograph  embodies  the  results  of  the  further  investigation  of 
amalgam  cells,  containing  not  only  the  two  metals  already  mentioned,  but 
also  thallium,  indium,  tin,  lead,  copper,  and  lithium.  The  first  section  of 
the  monograph  deals  with  thallium,  indium,  and  tin.  These  metals  are 
especially  interesting  because  they  are  respectively  univalent,  trivalent, 
and  (under  some  conditions)  quadrivalent.  Thallium  is,  moreover,  inter- 
esting in  its  chemical  behavior,  having  in  common  with  the  alkali-metals 
a  soluble  hydroxide,  carbonate,  and  sulphate,  while  on  the  other  hand 
resembling  lead  in  the  possession  of  an  insoluble  chromate  and  sulphide, 
and  a  slightly  soluble  chloride.  Indium  is  the  only  trivalent  metal  that 
forms  satisfactory  amalgams  for  the  present  purpose.1 

The  effort  was  made  to  attain  precision  sufficient  to  afford  an  adequate 
basis  for  the  desired  theoretical  considerations.  No  attempt  was  made  to 
attain  the  greatest  conceivable  precision,  because  such  an  attempt  would 
have  defeated  the  object  of  the  investigation,  by  so  limiting  the  variety 
of  results  obtainable  in  the  limited  time  as  to  have  restricted  their  gen- 
eralization. 

1  An  almost  complete  historical  review  may  be  found  in  the  monograph  of  Rich- 
ards and  Forbes  (Publication  of  Carnegie  Institution  of  Washington,  No.  56; 
Zeitschrift  fur  phys.  Chem.,  58,  683  [1907]).  A  paper  by  J.  Regnauld  (Compt. 
Rend.,  53,  533  [1861])  on  the  heat  of  amalgamation  of  the  metals  was  overlooked 
in  this  review,  and  the  date  of  Helrnholtz's  publication  (Monatsbericht  d.  kgl.  pr. 
Akad.,  Berlin,  1877,  p.  713)  was  accidentally  given  as  1882  instead  of  1877.  The 
reference  to  Lindeck's  work  is  Wied.  Ann.,  35,  311,  1888.  Mention  should  be  made 
of  a  mathematical  paper  by  Trevor  on  the  "  Electromotive  Force  of  Concentration 
Cells"  (Zeitschr.  Elektrochem.,  11,  681  [1905]).  While  this  paper  contains  inter- 
esting features,  experimental  verification  of  the  equation  deduced  therein  is  not 
possible  at  present.  In  a  recent  paper  published  after  most  of  the  work  embodied 
in  this  monograph  had  been  completed,  Carhart  discusses  the  Helmholtz  equation, 
as  applied  to  amalgam  cells.  (Phys.  Rev.,  March,  1908).  In  a  yet  more  recent 
paper  by  Hulett  and  De  Lury,  published  after  the  conclusion  of  the  present  work, 
the  work  of  Richards  and  Forbes  is  in  part  repeated  and  extended  to  more  dilute 
solutions.  In  so  far  as  the  two  investigations  overlap,  they  confirm  one  another 
(J.  Am.  Chem.  Soc.,  30,  1812  [1908]).  Another  theoretical  paper,  by  van  Laar 
(Arch.  Neerl.  d.  Sci.  ex.  et  nat.  [n]  vm,  296),  should  perhaps  be  mentioned. 


OF   THALLIUM,    INDIUM,   AND   TIN 


VALUES  OF  CONSTANTS. 


In  the  discussion  which  follows,  all  the  experimental  work  is  viewed  in 
the  light  of  three  mathematical  expressions  : 


<*> 


In  these  expressions, 

TT—  electromotive  force.  ct=  concentration  of  more  concen- 

F  —  Faraday's   equivalent  =  96,530  trated  amalgam. 

coulombs.  c2  =  concentration   of   less   concen- 

R  =  the  gas  constant.  trated  amalgam. 

r=the  absolute  temperature.  £7=  the  change  of  total  energy  in- 

v—  valence.  volved  in  the  dilution  of  the 

In  =  natural  logarithm  to  the  base  e.  amalgam. 

The  first  of  the  numbered  equations  is  the  well-known  expression  of 
Helmholtz  (sometimes  called  the  Gibbs-Helmholtz  equation)  ;  the  second 
contains  the  substance  of  the  proposal  of  von  Turin  and  G.  Meyer;  and 
the  third  is  the  suggestion  of  Cady  and  Lewis.  Both  of  the  last  two  may 
be  said  to  be  the  outcome  of  other  work  of  Helmholtz,  and  to  be  covered  by 
the  equation  of  Nernst.  Before  denning  the  quantities  whose  symbols  are 
given  in  the  foregoing  list,  it  may  be  well  to  say  a  word  about  these  funda- 
mental equations  themselves. 

Equation  (i)  needs  no  comment.  Equation  (2)  has  been  reached  in 
somewhat  different  ways  by  a  number  of  thinkers  ;  it  is  based  essentially 
upon  the  epoch-making  discussion  by  Helmholtz  of  the  concentration  cell.* 
The  forms  in  which  the  several  investigators  have  expressed  their  results 
appear  to  be  different,  although  they  express  essentially  the  same  idea; 
the  equation,  as  given  here,  is  not  exactly  like  that  of  any  of  them. 
Nernst,1  who  did  not  himself  at  first  apply  his  equation  to  cells  of  the  type 
under  consideration,  used  the  ratio  of  pressures  instead  of  the  ratio  of 
concentrations,  and  would  have  expressed  the  result  thus 


'Helmholtz,  Monatsberichte  d.  kgl.  pr.  Akad.,  Berlin,  1877,  p.  713.  Helmholtz's 
other  well-known  paper  on  the  thermodynamic  equation  numbered  (l)  above  was 
published  in  the  Sitzungsberichte  der  kgl.  pr.  Akad.,  Berlin,  in  February,  1882,  p.  22. 

'Nernst,  Zeitschr.  phys.  Chem.,  4,  129  (1889). 


4  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

In  this  equation  P  and  P'  represent  the  unknown  solution-pressures, 
whose  ratio  alone  is  to  be  inferred,  and  p  the  osmotic  pressure  of  the 
appropriate  ion  in  the  electrolyte.  The  latter  cancels,  being  common  to 

r>  rr*  r> 

both  electrodes,  and  the  expression  becomes  ir=—pln~^,.  If  no  other 
source  of  free  energy  other  than  osmotic  effect  is  present,  -—,  may  be  taken 

as  equal  to  —  and  the  equation  reduces  to  ours.     In  this  expression  the 

c* 

absence  of  association  in  the  dissolved  metal  is  assumed.  Both  Nernst's 
expression  and  that  given  above  are  calculated  on  the  basis  of  the 
gram-atom. 

On  the  other  hand,  von  Turin  *  and  Meyer  '  expressed  their  equations 
in  terms  of  concentration,  and  calculated  them  on  the  basis  of  the  electro- 
chemical equivalent  in  terms  of  grams  per  coulomb;  and  both  introduced 
the  molecular  weight  (M  or  p)  of  the  dissolved  metal  —  although,  to  be 
sure,  von  Turin  seems  to  have  accidentally  omitted  this  quantity  from  his 
final  statement.8  Their  equation,  reached  in  different  ways,  reads  T 


|,8.32r(2.3o3  toft,*)  = 


gram-atomic  weight 
Bearing  in  mind  the  fact  that  their  q  meant  =  -  -  -  —   and  that 

we  have  made  the  additional  assumption  (based  upon  the  measurements 
of  many  investigators)  that  M  =  gram-atomic  weight,  it  is  seen  that  their 
form  is  essentially  identical  with  that  given  above.  Our  form  will  be 
called  in  future  merely  "  the  concentration-equation,"  as  its  ascription  to 
any  one  author  might  under  the  circumstances  seem  invidious. 

Attention  should  be  called  to  the  fact  that  Helmholtz,  himself,  insisted 
that  his  original  concentration-equation  holds  true  only  when  there  is  no 
heat  of  dilution  involved  in  the  reaction,8  a  condition  reiterated  by  von 
Turin.  The  same  limitation  applies,  of  course,  to  the  equation  in  its 
present  simplified  form  ;  but  this  limitation  does  not  necessarily  apply  to  the 
equation  of  Nernst,  involving  solution-pressures  instead  of  concentrations. 
The  term  solution-pressure  must  be  interpreted  as  including  combined 
effect  of  all  the  tendencies  affecting  the  escape  of  the  dissolved  metal  from 

4  von  Turin,  Zeitschr.  phys.  Chem.,  5,  340  (1890)  ;  7,  221  (1891). 

SG.  Meyer,  Zeitschr.  phys.  Chem.,  7,  447  (1891). 

*  See  von  Turin  on  the  bottom  of  page  221,  Zeitschrift  fur  physikalische  Chemie, 
7  (1891). 

By  a  coincidence  of  misprints,  of  which  there  are  many  in  the  papers  of  both 
von  Turin  and  Meyer,  the  decimal  point  of  the  factor  19.1  has  been  misplaced  in 
each  case  and  reads  1.91.  This  mistake  was  inadvertently  copied  in  reporting  the 
history  of  their  work  in  Publication  56  of  the  Carnegie  Institution  of  Washington. 

8  Helmholtz,  Berliner  Monatsbericht,  November,  page  713  (1877). 


OF   THALLIUM,    INDIUM,   AND   TIN  5 

the  amalgam,  except  the  osmotic  pressure  of  the  ion  dissolved  in  the 
electrolyte.     Thus  P  and  P'   include  the   effect  of  the  chemical   free 

p 
energy  change  connected  with  dilution ;  and  if  such  exists  — -t  can  not  be 

equal  to  —  .     This  explanation  appears  to  be  necessary,  because  of  the 

Cl 

misconception    of   Carhart   concerning   the    significance   of   the    Nernst 
equation.' 

The  equation  of  Cady 10  and  of  Lewis  u  is  an  attempt  to  take  account  of 
the  heat  of  dilution,  thus  resolving  the  tendencies  P  and  P'  into  their  most 
important  components.  This  equation  may  only  be  supposed  to  hold  true 
when  there  is  no  change  of  heat  capacity  during  the  reaction.  Further 
explanation  may  be  deferred  until  the  present  research  has  been  described, 
when  a  still  more  recent  suggestion  of  Lewis,  concerning  the  application 

of  the  law  of  Raoult  ( —£  =  — ^ — )  to  osmotic  work,  will  also  be  con- 

\p       N+nJ 
sidered. 

Before  beginning  a  description  of  our  experimental  work  it  will  be  well 
to  consider  the  accuracy  with  which  the  various  quantities  in  the  equations 
are  defined. 

In  a  previous  contribution  from  this  laboratory"  the  results  of  Ray- 
leigh,18  F.  and  W.  Kohlrausch,"  Kahle,"  and  Patterson  and  Guthe,1'  con- 
cerning the  value  of  Faraday's  equivalent  F,  have  been  compared ;  and 
the  conclusion  was  reached  that  96,580  coulombs  are  associated  with  107.93 
grams  of  silver,  if  the  silver  is  weighed  in  a  form  free  from  mother-liquor, 
after  having  been  deposited  in  a  manner  avoiding  anode  complications. 
The  more  recent  work  of  Smith,  Mather  and  Lowry,  and  others,  has  not 
changed  our  opinion  on  this  point."  Since  Richards,  Collins  and  Heim- 
rod,18  and  Richards  and  Stull 19  have  established  the  universality  of  Fara- 
day's law  on  a  firmer  basis  than  ever,  the  same  value  can  be  used  for  a 
gram  equivalent  of  thallium  or  indium  with  reasonable  accuracy.  If  the 
atomic  weight  of  silver  is  taken  as  107.88,  a  value  probably  nearer  the 

•H.  S.  Carhart,  Phys.  Rev.,  26,  216  (1908). 

10  Cady,  Journ.  Phys.  Chem.  2,  551   (1898). 

11  Lewis,  Proc.  Am.  Acad.  35,  34  (1899). 

12  Proc.  Amer.  Acad.,  37,  415  (1902). 
"Phil.  Trans.,  175,  411   (1884). 
"Wied.  Ann.,  27,  I   (1886). 
15Wied.  Ann.,  67,  i   (1889). 

16  Phys.  Rev.,  7,  257  (1898). 

17  Smith,  Mather  and  Lowry,  Phil.  Trans.  Roy.  Soc.  London,  Series  A,  207,  545 
(1908);  also  see  especially  T.  W.  Richards,  Proc.  Am.  Acad.,  44,  91   (1908).    The 
Report  of  the  International  Conference  on  Electrical  Units  and  Standards,  "  Science," 
28  (1908),  recommends  F  =  96,540  for  the  same  atomic  weight  without  these  pre- 
cautions.   This  probably  amounts  to  about  the  same  thing. 

"Zeit.  phys.  Chem.,  32,  301  (1900). 
19  Proc.  Amer.  Acad.,  35,  123  (1899). 


6  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

truth,  the  value  F  must  be  diminished  by  0.05  per  cent,  and  becomes  96,530 
coulombs  per  gram  equivalent.  This  latter  value  is  used  in  the  work 
which  follows,  and  all  atomic  weights  also  are  referred  to  this  standard. 

The  symbol  v  represents  the  valency  of  the  metallic  ion  in  the  electrolyte 
of  the  cell.  Since  thallous  sulphate  and  indium  sulphate  were  used  as 
electrolytes  in  the  cells  of  thallium  and  indium  amalgams,  it  is  difficult  to 
conceive  how  the  valency  of  the  ions  of  thallium  and  indium  could  be 
other  than  I  and  3  respectively.  The  valency  of  tin  will  receive  especial 
consideration  when  that  metal  is  discussed;  in  our  experiments  it  was 
undoubtedly  2,  not  4. 

The  work  of  Daniel  Berthelot  "  probably  affords  the  most  accurate  value 
of  R,  which  we  may  express  conveniently  in  mayers.  A  mayer  is  the  heat 
capacity  which  is  warmed  I  degree  centigrade  by  I  joule.  According  to 
Berthelot's  work,  the  space  occupied  by  a  gram-molecule  of  a  perfect  gas 
at  760  mm.  pressure,  45°  latitude  at  the  sea-level,  may  be  taken  as  22.412 
liters  (the  atomic  weight  oxygen  being  16.000),  and  the  absolute  zero  at 
—  273.08°  C.  These  values  are  probably  accurate  at  least  to  within  0.05 
per  cent.  The  value  of  R  on  this  basis  will  be 

^76.00x13.596x980.6x22,412^     6 
273.08  XIOT 

T,  by  which  R  is  multiplied  in  the  formula,  is  the  temperature  of  the  cell 
referred  to  the  hydrogen  scale.  This  was  fixed  in  our  experiments  by 
means  of  four  exactly  known  thermometers.  Over  the  range  of  tempera- 
ture employed  in  the  following  measurements  these  readings  are  closely 
comparable  with  the  corresponding  thermodynamic  temperatures.  More- 
over, the  experimental  determination  of  the  temperature  to  within  0.01° 

would  fix  the  value  of  -J1  within  one  part  in  30,000,  a  degree  of  accuracy 

Jo 

far  greater  than  can  be  attained  with  the  rest  of  the  data  used  in  calculat- 
ing the  electromotive  forces. 

It  appears,  then,  that  the  values  of  v,  R,  T,  and  F  are  known  with 
considerable  accuracy,  and  it  now  remains  to  consider  the  concentration 

ratio  -£L.    An  error  of  o.i  per  cent  in  this  ratio  would  cause  an  error  of 

Ct 

o.ooooi  volt  in  the  electromotive  force,  and  it  is  clear  that  the  early  investi- 
gators have  not  determined  this  ratio  with  sufficient  accuracy.  If  a  weight 
w  of  amalgam  of  concentration  c±  is  mixed  with  a  weight  nw  of  mercury 
to  form  a  new  amalgam  of  concentration  c2,  it  is  not  permissible  in  accurate 
work  to  write 


*"Trav.  et  Mem.  du  Bureau  internat.  des  poids  et  mesures,  13,  113  (1903). 


OF   THALLIUM,    INDIUM,   AND   TIN  7 

as  seems  to  have  been  the  custom  of  previous  workers  in  this  field. 
Richards  and  Forbes  have  shown  the  necessity  of  applying  a  correction 
for  the  difference  in  density  of  the  two  amalgams  being  compared.  For 
example,  let  w  be  the  weight  of  an  amalgam  of  concentration  c^  diluted 
with  wHe  grams  mercury  to  form  a  new  amalgam  c2.  Now,  if  D^  and  D2 
are  the  densities  of  the  amalgams,  we  have 


Careful  determinations  were  made  of  the  densities  of  the  several  amal- 
gams at  various  concentrations;  and  corresponding  corrections  were 
applied  to  the  calculated  values  of  the  concentration  ratio.  These  determi- 
nations will  be  considered  later  in  their  proper  place.  The  densities  were 
all  measured  at  20°  ;  their  relative  values  undoubtedly  change  slightly 
with  the  temperature,  but  not  enough  to  affect  appreciably  the  calculation 
in  question. 

In  calculating  the  thermochemical  results,  one  18°  calorie  was  taken  as 
equal  to  4.181  joules.*1 

A  number  of  typical  cadmium  standard  cells,  containing  crystals  of 
cadmium  sulphate,  prepared  from  different  pure  materials  at  different 
times,  were  used  as  the  standard  of  electromotive  force.  As  these  all 
agreed  within  the  tenth  of  a  millivolt,  their  value  was  taken  as 

1.0184  —  0.00004  (t°  —  20°)  international  volts 
and  this  value  was  used  as  the  standard  of  electromotive  force.** 

"Callendar  and  Barnes,  Phil.  Trans.,  A,  199,  149  (1902). 

11  See  Report  of  International  Conference  on  Electrical  Units  and  Standards, 
1908—  published  in  many  places,  for  example,  "Science,"  28,  743  (1908). 


8  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

PREPARATION  OF  THE  AMALGAMS. 

The  thallous  sulphate  used  in  preparing  the  thallium  amalgams  was  a 
sample  which  had  been  many  times  recrystallized,  both  as  acid  sulphate 
and  as  sulphate.  The  original  preparation  had  been  of  a  high  grade  of 
purity.  The  indium  amalgams  were  prepared  from  a  sample  of  very  pure 
indium,  which,  through  the  kindness  of  Professor  L.  M.  Dennis,  of  Cornell 
University,  was  available  for  this  work.23  The  sample  in  question  had 
been  carefully  purified  for  use  in  the  determinations  of  the  atomic  weight 
of  indium,  although  it  was  not  the  purest  specimen  used  for  this  purpose, 
and  was  finally  fused  in  a  current  of  hydrogen.  It  contained  no  impurity, 
except  a  trace  of  iron.  Metallic  tin  was  obtained  by  the  electrolysis  of  an 
acid  solution  of  pure  stannous  chloride,  using  a  pure  carbon  anode.  The 
fine  needles  of  tin  were  washed  with  distilled  water  and  alcohol  and  dried 
in  a  desiccator  over  sulphuric  acid. 

Pure  mercury  was  obtained  as  follows:  Crude  mercury  was  shaken 
first  with  sulphuric  acid  to  remove  the  major  part  of  the  metallic  impuri- 
ties and  then  for  some  time  with  dilute  nitric  acid  and  mercurous  nitrate. 
The  sample  was  now  wholly  free  from  contamination  with  the  more 
electropositive  metals.  It  was  then  distilled  under  a  pressure  of  20  mm. 
of  hydrogen  in  an  apparatus  somewhat  similar  to  that  described  by 
Hulett.21  The  hydrogen  was  passed  through  three  towers,  containing 
solid  potash,  in  order  to  purify  and  dry  it.  The  entire  apparatus,  as  far 
as  the  connection  to  the  pump,  was  wholly  fused  together  in  order  to  avoid 
rubber  connections  or  glass  joints.  The  pipettes  in  which  the  mercury 
was  kept  were  themselves  used  as  the  receivers  of  this  still,  and  the 
mercury  was  sealed  in  them  without  for  an  instant  coming  in  contact  with 
the  air.  The  stopcock,  regulating  the  supply  of  gas  bubbling  through  the 
mercury,  was  lubricated  with  sirupy  phosphoric  acid.  The  mercury  thus 
obtained  must  have  been  very  pure.  Distillation  in  air,  recommended  by 
Hulett,  affords  an  excellent  means  of  oxidizing  other  metals  present;  but 
our  experience  leads  us  to  fear  that  the  product  contains  a  trace  of 
dissolved  oxygen.  Accordingly,  we  used  hydrogen  instead  of  air. 

The  water  used  in  making  up  the  solutions  was  distilled  twice,  first 
from  an  alkaline  permanganate  solution,  and  then  from  very  dilute 
sulphuric  acid. 

Since  amalgams  of  all  the  metals  studied  are  very  susceptible  to  oxida- 
tion, they  were  made  and  introduced  into  the  measuring  apparatus  wholly 
out  of  contact  with  the  atmosphere,  and  the  mercury  from  which  they 
were  made  was  never  allowed  to  come  into  contact  with  the  air  after  its 
distillation  in  rarified  hydrogen. 

33  For  details  of  purification  of  this  indium  see  Jour.  Amer.  Chem.  Soc.,  29  (1907). 
MZeit.  phys.  Chem.,  33,  611  (1900). 


OF   THALLIUM,    INDIUM,   AND   TIN  9 

It  was  found  that  the  thallium  amalgams  could  be  most  conveniently 
prepared  by  the  electrolysis  of  a  solution  of  thallous  sulphate,  using  a 
mercury  cathode.  Addition  of  ammonium  oxalate  prevented  the  formation 
of  peroxide  on  the  anode.  The  complete  apparatus  used  in  preparing  and 
transferring  the  amalgam  is  shown  in  fig.  i. 


Hydrogen 


Pump 


Fig.   I.  Apparatus  (or  Making  and  Preserving  Amalgams. 

The  amalgams  were  prepared  by  electrolysis  in  the  flask  H.  Connection 
was  made  to  the  mercury  cathode  by  means  of  glass  tube  passing  through 
the  stopper  carrying  the  wire  K.  The  anode  7  terminated  in  a  spiral  of 
platinum  wire.  The  anode  was  inclosed  in  a  small  linen  bag  (not  shown 
in  the  figure),  in  order  to  prevent  any  peroxide  which  might  be  formed 
from  falling  on  the  cathode.  The  amount  of  thallium  deposited  was 
measured  by  a  silver  coulometer  included  in  the  circuit.  The  coulometer 
was  of  the  form  used  by  Richards  and  Heimrod.  The  porous  cup  was 
cleaned  with  concentrated  nitric  acid  and  then  boiled  with  many  portions 
of  water  before  use.  The  anode  was  a  bar  of  pure  silver  which  had  been 
prepared  for  use  in  an  atomic  weight  research.  Care  was  taken  to  keep 
the  level  of  the  liquid  within  the  porous  cup  lower  than  that  outside  in 
order  to  prevent  outward  filtration.  An  amperemeter,  also  in  the  circuit, 
served  for  an  approximate  measurement  of  the  current  strength. 


10  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

A  weighed  amount  of  pure  mercury  was  run  into  the  flask  H,  which 
was  then  nearly  filled  with  a  saturated  solution  of  thallous  sulphate  con- 
taining about  ten  grams  of  ammonium  oxalate.  The  stopper  was  inserted, 
care  being  taken  that  the  cathode  and  the  tube  T  leading  to  the  flask  C 
were  immersed  in  the  mercury.  The  current  was  now  allowed  to  run 
until  the  desired  quantity  of  thallium  had  been  deposited.  The  time  neces- 
sary for  this  could  be  calculated  approximately  from  the  readings  on  the 
amperemeter.  On  breaking  the  circuit,  the  amalgam  was  immediately 
sucked  up  into  C  by  cautiously  opening  the  stopcock  S4.  The  platinum 
crucible  containing  the  deposited  silver  was  washed  with  water,  dried  at 
200°,  and  weighed.  From  the  weight  of  the  silver  deposited,  the  concen- 
tration of  the  amalgam  could  be  calculated. 

The  arrangement  employed  in  transferring  the  amalgams  was  essentially 
similar  to  that  used  by  Richards  and  Forbes.  Hydrogen,  prepared  from 
pure  hydrochloric  acid  and  zinc,  and  purified  by  passing  through  four 
towers  containing  concentrated  potassium  hydroxide  solution  and  dry 
fused  potash,  was  supplied  through  the  tube  G.  The  pipette  B  communi- 
cated through  A  with  either  the  hydrogen  supply  or  the  vacuum-pump. 
The  outlet  tube  of  B,  terminating  in  a  thick  capillary,  passed  through  a 
tightly  fitting  rubber  stopper  into  the  flask  C.  (The  rubber  stopper  had 
been  boiled  with  alkali,  thoroughly  washed  with  water  and  finally  covered 
with  soft  paraffin.)  The  flask  C  was  supplied  with  two  side  necks.  The 
tube  F  communicated  with  the  vacuum-pump,  while  T  was  bent  down 
and  passed  to  the  bottom  of  the  flask  H. 

The  whole  apparatus  being  thoroughly  clean  and  dry,  it  was  manipu- 
lated as  follows:  First  S±,  6\,  and  S6  were  closed  and  S2  and  S3  were 
opened ;  the  pressure  in  B  and  C  was  reduced  to  1 5  mm.  of  mercury,  and 
St  was  closed.  The  manometer,  R,  proved  that  the  apparatus  was  free 
from  leakage.  By  cautiously  opening  S6  the  system  was  now  filled  with 
hydrogen ;  and  the  exhaustion  and  filling  with  hydrogen  were  repeated 
three  or  four  times.  Care  was  taken  to  expel  the  air  in  the  capillary  also 
by  a  stream  of  hydrogen.  In  order  to  force  the  hydrogen  through  the 
shallow  layer  of  mercury  in  the  bottom  of  H,  the  pressure  in  H  was 
slightly  diminished  by  suction  through  S7.  After  the  amalgam  had  been 
drawn  up  into  C,  a  rapid  stream  of  dry  hydrogen  was  bubbled  through  it 
by  opening  S6  and  Sa,  at  the  same  time  maintaining  a  low  pressure  in  C. 
This  served  to  dry  the  amalgam  and  to  mix  it  thoroughly.  After  10  or  15 
minutes  S2  was  closed  and  the  system  was  allowed  to  fill  with  hydrogen. 
Sl  was  then  opened  and  B  exhausted.  By  opening  S5  the  amalgam  could 
be  drawn  up  into  B.  S5  was  finally  opened  and  normal  pressure  restored 
in  B,  which  was  then  sealed  off  at  A  by  using  a  small  blast  flame.  F  was 
cut  with  a  file  and  the  flask  C  detached.  The  capillary  tip  of  the  pipette- 


OF   THALLIUM,    INDIUM,   AND   TIN 


II 


like  tube  of  B  was  immediately  sealed  with  wax  to  protect  it  from  air. 
The  pipettes  were  kept  in  a  rack,  shown  in  fig.  2. 

Precisely  the  same  mode  of  procedure  was  followed  in  preparing  and 
protecting  the  electrolyte  used  in  the  cell.  The  stream  of  hydrogen  was 
allowed  to  bubble  through  C  for  some  time  to  remove  the  last  traces  of  air 
from  the  solution.  It  was  then  drawn  up  into  the  pipette  and  sealed  off 
as  before.  When  the  solution  was  wanted  its  weight  was,  of  course,  not 
sufficient  to  draw  it  out;  accordingly  the  following  method  was  used  to 
follow  it  up  with  hydrogen :  A  clean  rubber  tube,  delivering  a  stream  of 
pure  hydrogen,  was  slipped  over  the  drawn-out  portion,  and  the  tube  was 
then  broken ;  in  opening  the  stopcock,  the  solution  readily  flowed  out. 


Fig.   2.  Rack  with  Pipettes  containing  Amalgams. 

The  amalgams  of  indium  and  tin  were  prepared  in  the  same  apparatus. 
It  was  found  more  convenient  to  prepare  the  latter  amalgams  by  adding 
the  metals  directly  to  the  mercury  in  the  atmosphere  of  carbon  dioxide  in 
the  flask  H,  for  they  are  far  less  readily  oxidized  than  the  others ;  but 
afterwards  the  amalgam  was  treated  just  as  the  others. 


12  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID  AMALGAMS 

DENSITIES  OF  THE  AMALGAMS. 

It  has  been  pointed  out K  that  a  knowledge  of  the  densities  of  the  various 
amalgams  is  essential  in  order  to  fix  accurately  the  value  of  the  concen- 
tration-ratio in  calculating  the  theoretical  potentials  of  the  cells.  More- 
over, such  data  make  possible  the  calculation  of  the  contraction  or  expan- 
sion occurring  on  the  amalgamation  of  the  various  metals.  For  these 
reasons  numerous  determinations  were  made  of  the  densities  of  the  amal- 
gams of  thallium,  indium,  and  tin. 

The  pycnometer  used  was  of  the  Sprengel  type,  as  modified  by  Ostwald ; 
its  capacity  was  about  3  cc.  and  its  tubes  i  mm.  in  diameter.  Before  use  it 
was  thoroughly  cleaned  with  appropriate  reagents,  and,  after  washing  with 
water,  dried  by  suction.  The  weight  of  the  pycnometer  filled  with  mercury 
at  20°  was  then  carefully  determined.  Since  in  filling  the  pycnometer 
with  the  amalgams,  it  was  sometimes  difficult  to  adjust  the  contents  exactly 
to  the  marks,  the  weight  of  a  centimeter  length  of  mercury  in  the  capillary 
was  determined,  and  a  suitable  correction  was  applied.  The  length  of  any 
excess  in  the  column  of  amalgam  was  accurately  determined  with  dividers. 
Since  the  correction  was  small,  never  amounting  to  more  than  0.15  gram, 
the  difference  in  density  between  mercury  and  the  amalgam  would  cause 
no  appreciable  error.  All  the  densities  were  determined  at  20°.  The 
amalgams  used  in  these  determinations  were  prepared  in  the  manner 
already  described.  When  all  was  ready,  a  sufficient  quantity  of  the 
amalgam  was  run  out  into  a  small  weighing  bottle,  filled  with  carbon 
dioxide,  and  hastily  drawn  up  into  the  pycnometer.  By  working  in  this 
fashion,  no  serious  oxidation  occurred.  The  thread  of  mercury  was 
adjusted  only  after  the  pycnometer  had  been  in  a  thermostat  at  20.0°  for 
some  time. 

The  data  of  a  typical  determination  are  as  follows : 


Weight      of      pycnometer      and 

mercury    53.228 

Weight  of  pycnometer  alone 18.134 

Weight  of  mercury 35.094 


Weight  of  pycnometer  and  amal- 
gam      53-121 

Weight  of  pycnometer  alone 18.134 

Weight  of  amalgam 34.987 


The  density  of  mercury  at  20°  is  13.545,  therefore  the  density  of  the 
amalgam  is 

1^X13.545  =  13.504 

This  amalgam  contained  1.845  Per  cent  thallium. 

Table  I  contains  the  results  with  amalgams  of  thallium,  indium,  and  tin. 
There  are  given  also  imaginary  values  which  the  densities  would  have 
shown  if  no  contraction  or  expansion  had  taken  place  on  amalgamation. 

'"Richards  and  Forbes,  Publication  of  Carnegie  Institution  of  Washington,  No. 
50,  ii  (1900).  Also,  pp.  6  and  7  of  the  present  monograph. 


OF   THALLIUM,    INDIUM,    AND   TIN 


The  values  of  the  densities  of  the  pure  metals  used  for  this  calculation  are 
given  in  the  first  column  of  the  table.  The  value  for  the  density  of  pure 
indium  is  the  mean  of  two  closely  agreeing  determinations  made  by  us 
with  Professor  Dennis's  pure  sample  of  the  metal,  because  the  values 
previously  obtained,  7.421  by  Winkler  and  7.12  by  Thiel,  are  in  very  poor 
agreement.  Our  data  are  as  follows : 

First  Determination: 

Weight  of  pycnometer :  Grams. 

With  air-free  water  (20.0° ) 10.1338 

Alone    7.0012 

With  indium  alone 10.2568 

With  indium  and  water 12.9420 

Result :    Density    7.277 

Second  Determination: 
Weight  of  pycnometer : 

With  indium  alone 10.0045 

With  indium  and  water 12.7525 

Result :    Density   7.291 


The  mean  value  is  7.284. 
indium  is  found  to  be  7.277. 


Corrected  to  vacuum  the  true  density  of 


TABLE  i. — Densities  of  Amalgams. 


Metal. 

Per  cent  of 
solid  metal 
in  amalgam. 

Correct 
weight  of 
liquid  needed 
to  fill  pyc- 
nometer. 

Actual 
density  of 
liquid. 

Calculated 
imaginary 
density  of 
amalgam. 

Thallium  (density  11  .85)  

1.854 

34.987 

I3.504 

13.509 

I.4IO 

35-017 

I3.5I5 

13.520 

0-793 

35-049 

13.527 

13-530 

Indium  (density  7  28) 

I    020 

Q 

^3-334 

13  .324 

i  »yOT* 

1.430 
1.090 

34.703 
34.784 

13-394 
13.426 

13.380 
13.419 

0.928 

34.835 

13.446 

13-439 

0.770 
0.468 

34-867 
34-949 

13-457 
13.489 

13-455 
I3.490 

Tin  (density  7  29) 

O.45 

35.012 

13.513 

I3.493 

0.30 

35-027 

13.519 

13.510 

0.21 

35-053 

13.529 

13.519 

Mercury,  pure  (density  13.545) 

0 

35-095 

13-545 

13-545 

The  density  curves  for  the  thallium,  indium,  and  tin  amalgams  are 
shown  in  fig.  3.  The  dotted  lines  give  the  imaginary  values  that  would 
be  obtained  if  neither  expansion  nor  contraction  took  place  on  mixing. 
Indium  and  tin  contract  on  amalgamation,  while  in  the  case  of  thallium 
there  is  a  slight  expansion. 


ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 


1334 

036 

13.38 
13.40 
13.42 
13.44 
13.46 
13.48 

13.54 

'> 

/'/ 

/ 

/ 
// 

/ 

// 

/ 

// 

7 

In 

/  / 

? 

'*/ 

?_ 

/ 

/ 

6 

^Sn 

^~~ 

Tl_ 

^  —  - 

-0-^ 

/ 

7 

-•—  "^"-^ 





^-*** 

0.2  0.4  as  0.8  1.0  1.2  1.4  1.6 

Fig.  3.  Densities  of  Thallium,  Indium,  and  Tin  Amalgams. 

Densities  are  plotted  as  ordinates,  per  cents  by  weight  of  solute  in  amalgam  as  ab- 
scissae. The  continuous  lines  represent  actual  densities,  the  dotted  lines 
the  averaged  densities  of  the  components,  that  is,  the  density  which  the 
amalgam  would  have  possessed  if  there  had  been  no  change  of  volume  on 
mixing.  The  dotted  line  for  tin  coincides  essentially  with  that  for  indium. 


OF   THALLIUM,    INDIUM,    AND   TIN  15 

THE  CELL. 

The  multiple  cell  used  in  all  the  measurements  of  electromotive  force  is 
shown  in  fig.  4.  This  apparatus,  devised  by  Richards  and  Forbes,  must  be 
very  carefully  annealed,  for  even  at  the  best  the  glass  receptacle  is  very 
fragile.  The  body  of  the  vessel  is  used  to  hold  the  electrolyte ;  the  four 
cups  contain  the  amalgams  to  be  measured.  The  advantage  of  the  four 
cups  is  obvious :  six  different  measurements  may  be  made  at  one  filling, 
and  at  the  same  time  important  checks  can  be  secured  on  the  accuracy  of 
the  readings. 


Fig.  4.  Amalgams  in  Cell  ready  for  Potential  Measurement. 

The  glass  receptacle  was  carefully  cleaned  and  dried,  and  fused  at  A  to 
the  delivery  tube  of  an  apparatus  supplying  pure  hydrogen.  A  vacuum 
pump  was  now  attached  at  Sz  and  the  whole  cell  exhausted  as  far  back  as 
the  stopcock  S^  The  tops  of  the  tubes,  B,  C,  D,  and  E  were  closed  with 
small  pieces  of  rubber  tubing  and  glass  rod.  When  the  pressure  had  been 
reduced  to  about  20  mm.,  the  stopcock  S2  was  closed  and  the  cell  allowed 
to  fill  with  hydrogen  through  3\.  This  was  repeated  four  times.  The 
glass  rod  was  now  removed  from  one  of  the  tubes  and  the  fine  tip  of  a 
pipette,  containing  the  proposed  electrolyte,  inserted.  The  issuing  stream 
of  hydrogen  prevented  the  diffusion  of  air  into  the  cell.  When  the  vessel 
was  about  half  full  of  the  aqueous  solution,  the  pipette  was  withdrawn  and 
the  stopper  was  replaced.  In  the  same  manner  suitable  amounts  of  the 


l"6  ELECTROCHEMICAL   INVESTIGATION    OF   LIQUID   AMALGAMS 

various  amalgams  and  mercury  were  introduced  into  the  four  cups. 
Finally,  the  electrodes,  sealed  into  narrow  glass  tubes,  were  introduced — 
care  being  taken  that  the  platinum  points  did  not  touch  the  glass.  S^  was 
now  closed,  the  coil  broken  off  from  the  hydrogen  supply,  and  the  vacuum 
connection  removed  from  S2.  After  gentle  shaking  for  several  minutes, 
the  completed  cell  was  transferred  to  the  thermostat,  and  the  measure- 
ments soon  begun. 

Amalgams  prepared  thus  remained  bright  as  long  as  was  necessary  and 
showed  no  signs  of  oxidation.  It  is  evident  that  Hulett  and  De  Lury  did 
not  fully  read  the  somewhat  similar  description  by  Richards  and  Forbes, 
or  they  would  not  have  suggested  that  the  method  contained  faults  which 
existed  only  in  the  preliminary  work,  not  in  the  procedure  finally  adopted.24 

The  manner  of  adjusting  the  wires  connecting  the  potentiometer  to  the 
cell  should  be  mentioned.  In  the  first  trials  long  platinum  wires  dipping 
in  the  various  amalgams  were  connected  with  the  copper  wires  by  means 
of  mercury  cups.  The  junctions  of  unlike  metals  were  thus  outside 
of  the  thermostat — an  objectionable  feature.  Accordingly,  in  the  final 
measurements  only  a  short  length  of  platinum  wire  was  fused  in  the 
bottom  of  each  tube  dipping  into  the  cell,  and  above  this  was  placed,  inside 
the  tube,  a  drop  of  mercury.  The  copper  wires  were  now  pushed  down  the 
narrow  tubes  until  connection  was  made  with  this  drop.  The  contact  of 
unlike  metals  was  now  deep  in  the  cell  and,  being  at  constant  temperature, 
could  cause  no  disturbance. 

Most  of  the  potentials  were  measured  at  30°  and  o°,  and  many  of  the 
thallium  cells  were  also  measured  at  15°.  The  temperature  of  the  30° 
bath  was  kept  constant  by  means  of  a  sensitive  electrical  regulator.  A 
large  heating  coil  was  used  in  place  of  an  incandescent  lamp  as  the  source 
of  heat,  since  it  avoids  any  disturbing  effect  due  to  radiant  energy  when 
the  heater  is  in  frequent  operation.  The  temperature  of  this  bath  was 
always  constant  within  0.01°.  The  15°  bath  was  exactly  similar  except 
that  it  was  equipped  with  a  cold-water  coil  in  order  to  compensate  for  the 
higher  temperatures  of  the  surroundings.  For  the  zero  bath  a  metal 
trough  was  filled  with  clean,  finely  crushed  ice,  covered  with  distilled 
water.  This  trough  was  placed  in  a  larger  one,  the  space  between  being 
filled  with  ice,  and  the  box  in  turn  was  tightly  packed  in  sawdust.  This 
arrangement  gave  a  very  constant  temperature.  The  temperatures  of  all 
the  thermostats  were  determined  with  small  Beckmann  thermometers, 
capable  of  being  read  to  within  0.005°  ;  they  were  standardized  by  com- 
parison with  a  very  accurate  Reichsanstalt  thermometer,  taking  all  the 
precautions  necessary  for  ascertaining  the  temperature  to  within  o.oi.° 

M  Compare  Hulett  and  De  Lury,  Journ.  Am.  Chem.  Soc.,  30,  1809  (1908)  with 
Richards  and  Forbes,  Publication  of  Carnegie  Institution  of  Washington,  No.  56, 
page  40  (1906). 


OF   THALLIUM,    INDIUM,   AND   TIN  17 

THE  POTENTIOMETER. 

Considerable  time  was  spent  in  the  elaboration  of  a  suitable  potentiom- 
eter for  use  in  this  work.  The  arrangement  used  by  Richards  and 
Forbes,  while  probably  accurate  to  0.000005  of  a  volt,  was  complicated 
and  involved  troublesome  calibrations.  Moreover,  it  seemed  desirable  to 
dispense  with  the  one-volt  element  and  compare  the  drop  of  potential 
directly  with  a  standard  Weston  cell.  The  arrangement  finally  adopted  is 
shown  in  fig.  5.  It  was  elaborated  with  the  help  of  R.  N.  Garrod-Thomas, 
and  was  used  also  for  his  work,  to  be  described  later. 


E 


o  °    °  - 

o 

o 

o 

A    o 

o 

o 

o 

o 

o 

T 

T 

x 


Fig.  5.  The  Potentiometer. 

A  large  Daniel  cell  F  was  used  as  the  source  of  the  fall  of  potential. 
When  in  use,  it  was  found  best  to  keep  it  short-circuited  through  a  resist- 
ance of  about  300  ohms  in  the  box  E.  The  rough  box  D  was  so  adjusted 
that  the  fall  of  potential  between  the  points  U  and  V  was  equal  to  1.0184 
volts,  as  measured  against  the  normal  cell  H.  C  was  a  constant  resistance 
of  9000  ohms.  A  and  B  were  resistance  boxes  of  mi  ohms  each,  and 
MN  was  a  manganin  wire  of  1.063  ohms  resistance.  At  the  commence- 


l8  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

ment  of  a  measurement,  the  plugs  were  all  placed  in  the  box  A  and  all 
removed  from  B.  The  resistance  between  U  and  V  under  these  conditions 
was  10,112.06  ohms,  embracing  a  drop  of  potential  of  1.0184  volts,  as 
given  above.  By  removing  plugs  from  A  to  the  corresponding  place  in  B, 
in  order  to  keep  the  drop  of  potential  constant,  and  manipulating  the  slider 
X,  it  was  easy  to  compensate  the  potential  of  the  unknown  cell  by  opposing 
potential  tapped  from  the  box  A  and  the  slide-wire  bridge,  since  the  poten- 
tials measured  never  amounted  to  as  much  as  o.i  volt. 

Suppose  the  total  reading  of  the  box  A  and  the  slide  wire  to  be  a  ohms. 

Then  the  potential  of  the  cell  measured  would  be  -p  X  1.0184  volts. 

10,112.06 

The  factor     *'  I  ^    being  a  constant  value,  its  logarithm  was  found  once 

for  all,  and  entered  into  all  calculations. 

In  following  this  mode  of  procedure,  the  only  portion  of  the  resistance 
which  needs  very  accurate  calibration  is  the  box  A.  The  wire  MN  was 
65  cm.  in  length,  and  was  divided  by  a  scale  into  divisions  6.10  mm.  long, 
each  of  these  corresponding  to  the  millionth  of  a  volt.  Since  the  total  fall 
of  potential  in  the  wire  was  only  about  o.oooi  volt  and  preliminary  calibra- 
tion showed  it  to  be  very  uniform  in  resistance,  no  correction  was  deemed 
necessary  for  the  readings  of  this  scale  under  the  wire.  PQ  was  a  three- 
way  switch.  When  thrown  towards  P,  the  standard  cell  H  was  balanced 
against  the  fall  of  potential  between  U  and  V.  When  thrown  toward  Q, 
the  potential  was  ready  to  be  balanced  against  a  portion  of  the  bridge  M N 
and  box  A.  The  galvanometer  G  of  the  d'Arsonval  variety  was  manu- 
factured by  the  Leeds  and  Northrup  Company,  of  Philadelphia,  and  is 
designated  by  them  as  Type  H.  It  was  read  with  a  telescope  and  scale 
at  a  distance  of  60  cm.  .S  was  a  double-rocker  switch,  the  base  of  which 
was  a  thick  plate  of  ebonite.  It  was  so  arranged  that  the  galvanometer 
was  either  in  the  circuit  or  short-circuited  itself.  The  galvanometer  was 
extremely  sensitive,  and  when  short-circuited  it  returned  to  zero  without 
any  oscillations  whatever.  The  whole  potentiometer  with  the  exception 
of  the  galvanometer  was  placed  inside  of  a  large  glass  case  with  a  swing- 
ing door  in  order  to  avoid  disturbing  effects  from  changes  of  temperature 
and  impurities  in  the  atmosphere. 

The  apparatus,  as  described  above,  was  used  in  the  measurements  on 
thallium  amalgam  cells  and  was  easily  accurate  to  within  three  or  four 
millionths  of  a  volt.  Since  thallium  under  the  conditions  of  the  measure- 
ments was  univalent,  and  consequently  gave  comparatively  large  poten- 
tials, the  above  accuracy  was  fully  sufficient ;  but  in  the  case  of  trivalent 
indium,  which  for  equal  concentrations  gives  potentials  only  one-third  as 
large  as  those  of  a  univalent  metal,  even  greater  accuracy  was  desirable. 


OF   THALLIUM,    INDIUM,    AND   TIN  19 

As  has  been  previously  mentioned,  the  portion  of  the  bridge  wire  MN 
corresponding  to  one  ohm  was  divided  into  100  parts,  giving  direct  read- 
ings to  o.oooooi  volt  for  each  6  mm.  of  wire.  The  graduation  of  the 
instrument  was  therefore  adequate ;  improvement  was  to  be  attained  only 
by  eliminating  all  irregularities ;  and  prominent  among  these,  as  every  one 
knows,  are  thermoelectric  effects  due  to  junctions  of  dissimilar  metals. 

Two  ways  of  suppressing  thermoelectric  effects  are  available:  one,  to 
use  only  one  metal ;  the  other,  to  keep  the  temperature  the  same  through- 
out. The  latter  method  was  in  the  present  case  the  more  convenient.  It 
was  at  first  found  that  the  temperature  at  the  two  ends  of  the  glass  case 
containing  the  potentiometer  differed  by  as  much  as  0.5°.  Part  of  this 
difference  was  traced  to  the  proximity  of  an  incandescent  light,  which 
was  removed ;  but  there  still  remained  a  considerable  variation.  This  was 
finally  overcome  by  the  use  of  a  small  revolving  fan  which  was  attached 
to  an  axle  run  through  one  of  the  corners  of  the  case  and  driven  at  high 
speed  by  a  motor.  Thus  the  air  was  stirred  and  kept  at  the  same  tempera- 
ture throughout.  Contact  of  the  operator's  hand  with  the  bridge  slide 
was  obviated  by  the  use  of  two  cords  attached  to  opposite  sides  of  X  and 
passed  through  small  holes  in  the  ends  of  the  case ;  and  the  final  adjust- 
ment was  made  on  the  bridge  with  the  case  closed.  In  this  way  another 
frequent  source  of  irregularity  was  avoided  and  the  readings  were  im~ 
proved.  The  room  in  which  all  the  apparatus  was  placed  was  kept  as 
constant  in  temperature  as  possible. 

In  seeking  for  the  causes  of  the  yet  remaining  fluctuations,  it  was  found 
that  the  galvanometer  was  influenced  by  the  proximity  of  the  observer, 
and  even  more  so  by  heat-effects  due  to  the  operation  of  the  rocker  switch 
S  with  the  hand.  Therefore,  the  galvanometer  was  removed  some  dis- 
tance from  the  apparatus  and  screwed  against  a  very  firm  wall,  the  con- 
nections being  made  by  insulated  copper  wires  incased  in  glass  tubes.  The 
case  of  the  galvanometer  was  packed  in  felt  and  covered  with  a  sheath 
of  copper,  a  small  hole  permitting  a  view  of  the  mirror ;  and  the  instru- 
ment was  read  by  a  telescope  and  scale  placed  at  a  distance  of  about 
130  cm.  The  rocker  switch  5"  was  placed  inside  the  case  and  operated 
from  outside  by  means  of  a  long  cord,  the  observer  being  seated  at  the 
telescope  some  distance  away. 

The  resistance  box  A  was  standardized  by  substitution.  A  sensitive 
Wheatstone  bridge  was  used  and  the  corrections  on  the  various  resistances 
were  determined  and  tabulated  exactly  as  if  they  were  weights.*7 

Only  two  of  the  corrections  thus  found  were  as  much  as  o.oi  ohm,  and 
since  each  o.oi  ohm  corresponds  to  very  nearly  o.oooooi  volt,  it  is  easily 
seen  that  all  others  were  negligible.  The  two  in  error  were  the  300  and 

"Richards,  Proc.  Am.  Chem.  Soc.,  22,  144  (1900). 


20  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

400  ohm  coils ;  and  the  deviation  of  these  amounted  to  only  0.000002  and 
o.oooooi  volt  respectively.  The  boxes  B  and  C  were  of  the  same  quality 
as  A  and  a  preliminary  standardization  showed  them  to  be  fully  as  accu- 
rate. Since  the  resistances  in  B  and  C  need  be  known  only  one-tenth  as 
accurately  as  those  in  A,  any  corrections  on  these  boxes  would  be  super- 
erogatory. The  one  important  point,  that  1000  ohms  in  A  should  be 
exactly  one-ninth  of  the  9000  ohms  in  B,  within  o.oi  per  cent,  was  demon- 
strated. 

The  standard  Weston  cells  were  made  up  from  pure  material  as  recom- 
mended by  Hulett.  These  cells  were  compared  with  one  another  and  also 
with  three  similar  cells  kindly  loaned  by  Dr.  H.  L.  Frevert.  They  all 
furnished  the  same  value  to  within  o.oooi  volt  at  20°,  and  for  their  value 
the  electromotive  force  1.0184  was  accordingly  assumed. 

The  improved  potentiometer  described  above  appeared  to  be  accurate  to 
within  a  microvolt  (o.oooooi  volt) — a  high  degree  of  precision. 

ELECTROMOTIVE  FORCE  BETWEEN  THALLIUM  AMALGAMS. 

With  the  apparatus  and  materials  which  have  been  described,  measure- 
ments upon  a  variety  of  amalgams  were  executed.  The  description  of  a 
preliminary  experiment  will  be  given  in  detail,  in  order  that  the  method 
may  be  more  thoroughly  understood.  Amalgam  I  was  prepared  in  the 
closed  apparatus  by  depositing  into  180.557  grams  of  mercury  the  amount 
of  thallium  equivalent  to  0.9473  grams  of  silver  (deposited  in  a  coulometer 
in  the  same  circuit),  that  is  to  say,  1.7915  grams  of  thallium,  if  silver  and 
thallium  are  assumed  to  have  the  atomic  weights  of  107.88  and  204.03 
respectively.  Hence  the  amalgam  contained  0.9822  per  cent  of  thallium 
by  weight. 

One  portion  of  this  amalgam  was  introduced  into  one  cup  of  the  multiple 
cell,  and  another  weighed  portion  was  introduced  out  of  contact  with  air 
into  another  cup,  being  diluted  by  the  addition  of  a  weighed  amount  of  the 
pure  mercury,  which  had  been  preserved  in  hydrogen  as  previously 
described.  The  second  cup  contained  36.513  grams  of  mercury,  and 
received  25.721  grams  of  amalgam.  It  is  easy  to  calculate  that  the  dilute 
amalgam  must  have  contained  0.4059  per  cent  of  thallium.  In  order  to 
mix  thoroughly  the  amalgams  and  mercury  in  the  second  cup,  the  cell  was 
gently  shaken  for  some  time,  great  care  being  taken  to  avoid  any  splashing 
from  one  cup  to  another.  The  cell  was  then  introduced  into  the  30°  ther- 
mostat and,  after  it  had  acquired  the  temperature  of  the  bath  the  readings 
were  begun.  Two  measurements  of  the  cell  gave  values  of  25.235  and 
25.238  millivolts  respectively,  in  mean  25.237. 

The  potential  remained  very  constant  over  a  considerable  interval  of 
time.  Two  entirely  separate  measurements  taken  with  the  same  cell  48 


OF   THALLIUM,    INDIUM,   AND   TIN  21 

hours  later  gave  the  values  25.231  and  25.243,  in  mean  25.237,  exactly  the 
same  as  before.  In  subsequent  work  the  agreements  were  of  this  order 
of  accuracy ;  usually  average  values  alone  will  be  given. 

It  is  worthy  of  remark  in  this  connection  that  the  electrolyte  was  not 
found  to  be  the  least  alkaline  to  phenolphthalein  after  thus  standing  for 
48  hours  over  a  thallium  amalgam.  This  fact  is  very  satisfactory,  not  only 
with  regard  to  thallium,  but  also  in  its  implication  concerning  the  probable 
integrity  of  amalgams  of  less  easily  oxidized  metals,  whose  oxides  are  less 
easily  detected. 

It  is  interesting  to  compare  the  result  with  the  ideal  value  calculated 
from  the  gas  law.  The  theoretical  potential,  calculated  according  to  the 
formula 

T-8-3i6x  (273-090)  x  2.3026  .q, 

96,530  *  Cn 

is  23.064  millivolts.  This  is  2.183  millivolts,  or  nearly  10  per  cent,  less 
than  the  observed  value  25.237. 

Having  thus  cleared  the  way  by  this  preliminary  work,  four  series  of 
more  accurate  measurements  were  made.  Four  multiple  cells  containing 
thallium  amalgam,  designated  A,  B,  C,  and  D,  were  prepared.  In  each 
case  an  amalgam  prepared  electrolytically  was  placed  in  cup  I ;  and  cups 
2,  3,  and  4  were  filled  with  the  same  amalgam  diluted  (in  an  atmosphere  of 
hydrogen)  with  weighed  amounts  of  mercury. 

The  "  parent  amalgam  "  in  cups  Ai  and  Bi  was  made  by  depositing  in 
197.33  grams  of  mercury  the  amount  of  thallium  equivalent  to  0.4290  gram 
of  silver.  This  amalgam  was  diluted  as  follows : 

grams  of  amalgam.  grams  of  mercury. 

13.272  +  82.933  in  A2 

15.679  4L938  A3 

23.710  32.791  62 

6.838  97-483  63 

11.736  83.642  64 

The  "  parent  amalgam  "  in  cup  Ci  was  made  by  depositing  in  168.361 
grams  of  mercury  the  amount  of  thallium  equivalent  to  1.6738  grams  of 
silver.  This  amalgam  was  diluted  as  follows : 

grams  of  amalgam.  grams  of  mercury. 

12.487  +31.420  in  €2 

10.710  75-495  C3 

10.448  112.095  C4 

Finally  the  "  parent  amalgam  "  in  cup  Di  was  made  by  depositing  in 
213.65  grams  of  mercury  the  amount  of  thallium  equivalent  to  0.2289 
grams  of  silver.  This  amalgam  was  diluted  as  follows : 

grams  of  amalgam.  grams  of  mercury. 

14.967  +29.589  inD2 

8.851  75453  D3 

9.461  122.984  D4 


22 


ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 


The  electrical  measurements  made  with  these  amalgams  are  summarized 
in  table  2,  together  with  the  theoretical  values  calculated  upon  the  assump- 
tion that  the  gas  law  applies  with  exactness,  according  to  the  concen- 
tration equation: 

RT  .   cm 


TABLE  2.  —  Electrical  Measurements  of  Thallium  Amalgams. 


Designation 
of  cup 
containing 
amalgam. 

Approxi- 
mate 
per  cent  of 
thallium  in 
amalgams. 

Exact 
value  of 

'«•£_: 

Electromotive  force  between  each  pair  of  cups,  in  millivolts. 

0°C. 

15°C. 

30°C. 

Observed. 

Theo- 
retical. 

Observed. 

Theo- 
retical. 

Observed. 

Theo- 
retical. 

Ai  

0.410  , 

O.III     | 

0.0565* 
0.410  , 
0.172  1 

0.05I2J 

0.0269 

1.8456-, 
0.5249! 

0.2294  j 

0.1575^ 

0.220    -j 
0.074    1 
0.0231  | 
0.0157^ 

0.56502 
0.29408 

0.37694 
0.53272 
0.27338 

0.54518 
0.35943 
0.16340 

0.47203 
0.50556 
0.16729 

3L543 
16.360 

30.608 
15-080 

33.166 

17.238 

32.290 
16.858 

34.810 

18.110 

23-523 
32.408 
16.531 

37.134 
22.610 
10.090 

28.064 
30.592 
10.114 

33-971 
17-735 

22.664 
32.026 
16.436 

32.775 

21.610 

9.824 

28.379 
30.455 

10.058 

A2  

A3  

Bi  

B2  

83  

B4  
Ci  

C2  

C3  
C4  
Di  

D2  

D3  
D4  

33.897 
20.485 
9.II8 

29.533 
19.471 
8.852 

35-5" 
21.530 
9.601 

31.155 
20.541 
9.338 

The  measurements  with  cell  B  at  the  lower  temperatures  were  unsatisfactory, 
and  were  rejected;  cell  D  was  measured  only  at  30°. 

Each  observed  figure  is  the  mean  of  at  least  three  measurements.  For 
example,  the  Di-D2  was  found  to  have  a  potential  of  28.969  millivolts 
by  direct  measurement.  Di-D3  was  found  to  be  59.551,  and  D2-D3, 
30.596.  Subtracting,  we  find  again  D  1-02  =  28.95 5.  ^n  the  same  way, 
by  subtracting  the  observed  value  for  D2-D4  from  that  for  Di-D4,  the 
value  28.969  is  found.  The  mean  value  28.964  is  given ;  the  same  practice 
was  adopted  in  all  cases. 


OF   THALLIUM,    INDIUM,    AND   TIN  23 

The  difference  between  the  observed  and  the  ideal  values  is  usually 
great;  in  the  case  of  the  concentrated  cell,  Ci-C2,  it  amounts  to  13  per 
cent.  Further  study  of  the  figures  shows  that  as  the  dilution  is  increased, 
this  difference  between  the  observed  and  calculated  potentials  diminishes, 
becoming  only  about  0.6  per  cent  in  the  case  of  the  very  dilute  cell  D3-D4. 
Deviations  from  the  theoretical  are  always  positive ;  the  cell  always  gives 
a  potential  higher  than  the  value  computed  simply  from  its  concentrations. 
Cells  of  thallium  amalgams  thus  appear  to  behave  in  a  fashion  similar  to 
those  of  cadmium  with  increasing  dilution,  although  in  the  case  of  the 
thallium  cells  the  deviations  are  larger.  Zinc  varies  in  the  opposite 
direction. 

The  results  of  these  measurements  and  calculations  are  plotted  graphi- 
cally below  according  to  the  method  employed  by  Richards  and  Forbes, 
which  affords  a  convenient  method  of  noting  the  departure  of  the  cells 
from  the  gas  law.  In  fig.  6  there  are  plotted  as  abscissae  the  logarithms  of 
the  volumes  occupied  by  a  given  weight  of  amalgamated  thallium,  taking 
the  volume  of  the  most  concentrated  amalgam  in  cup  Ci  as  unity.  The 
progress  of  the  curve  in  the  direction  of  ordinates  between  the  points 
corresponding  to  any  two  volumes  indicates  the  extent  of  the  deviation 
from  the  theory  of  the  electromotive  force  of  the  cell  made  from  the  two 
indicated  amalgams.  The  curve  is  built  up  by  plotting  first  the  results 
with  cell  C,  then  those  with  cells  A  and  B,  and  finally  those  with  cell  D. 
In  each  case  as  the  drawing  progressed  the  "  parent  amalgam "  was 
started  at  its  proper  concentration  on  the  curve  already  drawn ;  and  this 
proceeding  of  necessity  fixed  the  other  points  obtained  from  that  particular 
cell.  If  into  each  cell  a  two-phase  amalgam,  having  a  constant  potential, 
had  been  introduced,  according  to  the  excellent  suggestion  of  Hulett  and 
De  Lury,  the  construction  of  this  curve  would  have  been  somewhat  facili- 
tated ;  but  the  final  result  would  have  been  identical.  In  this  case  greater 
care  about  perfect  constancy  of  temperature  would  have  been  necessary. 
The  regularity  of  the  curve  affords  strong  evidence  of  the  accuracy  of  the 
measurements. 

The  curve  for  the  thallium  amalgams,  like  those  for  both  zinc  and 
cadmium,  shows  that  as  dilution  is  increased  the  potential  of  any  cell 
approaches  nearer  and  nearer  to  the  requirement  of  the  simple  concentra- 
tion law ;  that  is  to  say,  the  slant  of  the  curve  becomes  less  and  less.  Com- 
plete horizon tality  would  indicate  complete  fulfilment  of  the  gas  law.  The 
regular  form  of  the  curve  indicates  the  absence  of  oxidation  in  the  more 
dilute  amalgams,  one  of  the  most  insidious  sources  of  error  in  this  sort  of 
work.  Thallium  amalgams  are  extremely  sensitive  to  oxidation  and  its 
elimination  in  these  measurements  is  a  source  of  gratification. 

The  results  depicted  by  this  curve  will  be  discussed  later  in  connection 
with  the  results  for  the  other  metals. 


24  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

+  7 


+  1 


Iog4        Iog8         log  16       log3Z      Iog64      log  128     log  256 
Fig.  6.  The  Deviations  of  the  Electromotive  Force  of  Thallium  Amalgams. 

Deviations  from  the  expression  »  =  ^F  '*  £7 are  Plotted  in  millivolts  as  ordinates, 
the  logarithms  of  the  concentration  ratios  as  abscissae.  The  most  concen- 
trated amalgam  contained  1.85  per  cent  by  weight  of  thallium  and  98.15 
per  cent  by  weight  of  mercury.  A  horizontal  line  on  the  diagram  would 
indicate  complete  fulfilment  of  the  concentration  law.  This  curve  is  almost 
if  not  quite  independent  of  temperature,  at  least  between  o*  and  30°. 


OF   THALLIUM,    INDIUM,   AND   TIN 


ELECTROMOTIVE  FORCE  BETWEEN  INDIUM  AMALGAMS. 

Amalgams  of  indium  were  now  studied  in  the  same  manner.  They  had 
been  prepared  in  the  fashion  described  on  page  9,  and  all  the  dilutions 
were  made  inside  the  cell  in  an  atmosphere  of  hydrogen  with  the  same 
precautions  as  in  the  case  of  thallium.  Density  corrections  were  applied 
in  the  calculation  of  the  concentration  ratio. 

Three  parent  amalgams,  Ei,  Fi,  and  Gi,  were  prepared.  The  first,  El, 
contained  3.0014  grams  of  indium  dissolved  in  152.783  grams  of  mercury; 
the  second,  Fi,  23.276  grams  of  this  amalgam  with  116.472  grams  more  of 
mercury,  and  the  third,  Gi,  contained  40.812  grams  of  Fi  with  72.926 
grams  more  of  mercury. 

These  "  parent  "  amalgams  were  diluted  as  follows : 


grams  of 
amalgam. 

10.368  Ei 

9-732   El 
8.074   El 
11.727  Fi 

grams  of 
mercury. 

+    41.883 
+    68.490 
+  123.133 
+    36.564 

in   E2 
E3 
£4 

F2 

grams  of 
amalgam. 

8.498   Fi 

8-543  Fi 
8.177  Gi 
9.328  Gi 

grams  of 
mercury. 

+    71.897 
-j-  Il8.68o 
+    58.144 
+  102.808 

in    Fj 
F4 

G2 

G3 

The  measurements  of  electromotive  force,  and  the  theoretical  values 
calculated  from  the  concentration  law,  are  given  in  table  3. 

TABLE  3.— Electrical  Measurements  of  Indium  Amalgams. 


Electromotive  force  between  each  pair  of  cups,  in  millivolts. 

Designation 
of  cup 
containing 
amalgam. 

percent  of 
indium  in 
amalgams. 

Exact 
value  of 

*  Z 

0°C. 

30°C. 

Observed. 

Theo- 
retical. 

Differ- 
ence. 

Observed. 

Theo- 
retical. 

Differ- 

cnce. 

El  

1.92     i 

0.69705 

14-455 

12.587 

1.868 

15.786 

13.967 

I.8I9 

E2  

0.384 

0.20III 

3.823 

3.631 

0.192 

4-23I 

4.030 

0.201 

E3  

0.242 

0.30466 

5.692 

5-501 

O.I9I 

6.287 

6.106 

O.lSl 

E4  

0.120 

Fi  

0.319 

0.6l38l 

H.387 

II.083 

0.304 

12.616 

12.301 

0.315 

F2  

0.078 

0.36079 

6.588 

6.515 

0.073 

7-3II 

7.231 

0.080 

F3  

0.034 

0.19750 

3.666? 

3.566 

O.IOO? 

3-989 

3.958 

0.031 

F4  

0.021 

Gi  

0.016  ) 

0.31887 

5-775 

5-758 

0.017 

6.411 

6.390 

0.021 

G2  

0.008 

O.I094I 

3-035 

3-003 

0.032 

3-430 

3-390 

0.040 

G3  

0.00     ' 

26 


ELECTROCHEMICAL   INVESTIGATION    OF   LIQUID  AMALGAMS 


Comparison  of  the  observed  and  calculated  potentials  of  the  indium 
amalgam  cells  shows  the  behavior  of  these  cells  to  be  similar  to  those  of 
thallium,  but  in  a  less  degree.  The  cells  with  concentrated  amalgams  show 
considerable  deviation  from  the  theoretical  value,  not  so  much,  however, 
as  with  thallium  amalgams  of  the  same  concentration.  On  the  other  hand, 
at  great  dilutions  the  agreement  between  the  observed  and  calculated 
values  is  exceedingly  close.  The  cell  Gi-G2  differs  by  only  0.000019  volt 
or  0.3  per  cent  from  the  theoretical  potential. 

The  significance  of  the  results  of  these  measurements  can  best  be  illus- 
trated by  the  same  sort  of  curve  as  was  employed  in  the  case  of  thallium 
amalgams.  The  curve  for  indium  amalgams  is  shown  in  fig.  7.  As  before, 
the  common  logarithms  of  the  concentration  ratios  are  plotted  as  abscissae 
and  the  value  of  the  deviations  from  the  simple  concentration  law  as 
ordinates.  The  sign  of  curvature  is  the  same  as  with  thallium,  since  both 
deviate  in  the  same  direction  from  theory. 

The  significance  of  this  curve  also  will  be  discussed  later. 


+  3 


-H 


logZ        Iog4        Iog8        log  16         Iog33      Iog64      logIZS       Iog256 
Fig.  7.  The  Deviation*  of  the  Electromotive  Force  of  Indium  Amalgam*. 


Deviations    from    the    expression 


are    plotted    in    millivolts    as    ordinates. 


the  logarithms  of  the  concentration  ratios  as  abscissae.  The  most  concen- 
trated amalgam  contained  1.92  per  cent  by  weight  of  indium  and  98.08 
per  cent  by  weight  of  mercury.  A  horizontal  line  on  the  diagram  would 
indicate  complete  fulfilment  of  the  concentration  law.  This  curve  is  almost 
if  not  quite  independent  of  temperature,  at  least  between  o*  and  30°. 


OF   THALLIUM,    INDIUM,   AND   TIN 


ELECTROMOTIVE  FORCE  BETWEEN  TIN  AMALGAMS. 

The  tin  amalgams  were  prepared  in  a  manner  similar  to  that  employed 
with  indium.  The  electrolyte  used  in  the  cells  was  a  solution  of  stannous 
chloride,  about  half  normal.  Before  use  it  was  allowed  to  stand  over  pure 
tin  and  was  then  preserved  under  hydrogen.  Great  care  was  taken  to 
insure  the  absence  of  stannic  compounds. 

Since  concentrated  tin  amalgams  deposit  a  solid  phase  on  cooling  to  o°, 
the  first  series  of  measurements  were  performed  by  the  dilution  of  an 
amalgam  containing  0.66  per  cent  by  weight  of  tin — less  than  half  of  the 
higher  concentration  used  by  Cady.  As  even  this  was  found  to  separate 
a  solid  at  o°,  another  series  was  made  beginning  with  an  amalgam  con- 
taining only  0.21  per  cent  of  tin. 

The  data  concerning  the  preparation  and  dilution  of  these  amalgams 
were  as  follows:  1.0766  grams  of  metallic  tin  were  dissolved  in  161.161 
grams  of  mercury  to  make  amalgam  Hi.  This  was  diluted  as  follows : 


grams  of  amalgam. 

17-351 
I3-279 
10.391 


grams  of  mercury. 

+  39-593 
+  99.824 
+  I47-265 


in  H2 
H3 
H4 


The  more  diluted  series  was  made  from  a  "  parent "  amalgam  obtained 
by  dissolving  0.3116  grams  of  tin  in  149.021  grams  of  mercury.  From 
this  were  prepared: 


grams  of  amalgam. 

18-537 
16.436 
9.919 


grams  of  mercury. 

+  44.845 
+  II3-3I2 
+  117-947 


in  J2 


TABLE  4. — Electrical  Measurement  of  Tin  Amalgams. 


Electromotive  force  between  each  pair  of  cups,  in  millivolts. 

tion  of 
cup  con- 

mate 
per  cent  of 

Exact 
value  of 

1         Cm 

0°C. 

30°C. 

taining 
amalgam. 

amalgams. 

l0gc. 

Observed. 

Theo- 
retical. 

Difference. 

Observed. 

Theo- 
retical. 

Difference. 

Hi.... 

0.66 

0.51495 

7.632 

13-949 

-6.317 

I3.I82 

15.480 

-2.208 

H2.... 

0.20 

0.41401 

I0.6I4 

11.213 

-0.599 

11.820 

12.447 

-0.627 

H3.... 

0.077 

Ji  

0.210  i 

0.53655 

I3.6l2 

I4.532 

—0.920 

15.156 

16.128 

-0.972 

J2  

0.061 

0.36025 

9.548 

9.758 

-0.210 

10.622 

10.829 

-0.207 

J3  

0.027 

0.21345 

5.715 

5.781 

-0.066 

6.371 

6.416 

-0.045 

J4  

0.016 

ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 


Examination  of  these  results  shows  that  the  observed  potentials  of  the 
amalgam  cells  of  tin,  like  those  of  all  the  other  metals  thus  far  studied, 
approach  the  theoretical  requirements  more  and  more  closely  as  the  dilu- 
tion is  increased.  The  results  are  depicted  graphically  by  the  curve  in 
fig.  8.  It  should  be  noted  that  the  sign  of  curvature  is  exactly  the  reverse 
of  that  of  the  otherwise  similar  curves  obtained  with  cadmium,  thallium, 
and  indium  amalgams,  since  tin  amalgams  deviate  in  the  opposite  direction 
from  theory.  In  this  respect  tin  is  similar  to  zinc. 


-2 


-3 


log  a  Io44  logS  log  16  log3Z  log  64 
Fig.  8.  The  Deviations  of  the  Electromotive  Force  of  Tin  Amalgams. 
Deviations  from  the  expression  IT  =  ^^  /»  c-±  are  plotted  in  millivolts  as 

ar  c-2 

ordinates,  the  logarithms  of  the  concentration  ratios  as  abscissae. 
The  most  concentrated  amalgam  contained  0.66  per  cent  by  weight 
of  tin  and  99.34  per  cent  by  weight  of  mercury.  A  horizontal 
line  on  the  diagram  would  indicate  complete  fulfilment  of  the 
concentration  law.  This  curve  is  for  30°.  The  most  concentrated 
amalgam  separates  solid  at  o°. 

In  the  case  of  the  tin  amalgam  cells  complete  exclusion  of  oxygen  is 
necessary,  not  only  on  account  of  the  amalgams,  but  also  in  order  to 
insure  the  stability  of  the  electrolyte,  since  stannous  chloride  when  exposed 
to  the  air  quickly  becomes  basic  according  to  the  equation  : 

3$>nC\2  +  y2  O2  +  H2O=2SnClOH  +  SnCl4 

When  the  solution  is  in  contact  with  tin  amalgam  in  the  air  this  reaction 
proceeds  very  rapidly,  perhaps  because  the  stannic  chloride  is  reduced  by 
the  amalgam.  The  formation  of  stannic  chloride  would  be  expected  to 
lower  the  potential,  and  the  constancy  observed  in  the  values  of  the  various 
cells  proves  the  complete  elimination  of  any  such  disturbing  effect. 


OF   THALLIUM,    INDIUM,    AND   TIN  2Q 

With  the  idea  of  testing  the  effect  of  stannic  chloride,  but  without  much 
hope  of  obtaining  results  fully  corresponding  to  a  quadrivalent  ion,  a 
further  attempt  was  made  to  measure  a  tin  amalgam  concentration  cell, 
using  an  electrolyte  containing  at  first  pure  stannic  chloride.  Pure  tin  was 
dissolved  in  aqua  regia  and  the  nitric  acid  was  removed  by  boiling 
repeatedly  with  fresh  portions  of  hydrochloric  acid.  The  solution  was  then 
diluted  with  water,  most  of  the  free  acid  was  neutralized  with  sodium 
hydroxide,  and  the  solution  containing  all  its  tin  in  the  state  of  highest 
oxidation  was  placed  in  the  cell. 

No  constant  readings  could  be  obtained  with  any  of  the  tin  amalgams 
under  these  conditions.  Evidence  was  obtained,  however,  that  this  electro- 
lyte tended  to  give  lower  potentials  than  those  obtained  with  stannous 
chloride.  For  example,  with  a  cell  whose  calculated  potential  would  be 
0.01605,  if  the  tin  were  quadrivalent,  and  0.0321,  if  bivalent,  a  value  of 
0.0262  was  obtained.  Clearly,  as  we  had  expected,  ionized  quadrivalent 
tin  is  not  in  a  state  of  electrochemical  equilibrium  with  tin  amalgam. 

Cady28  supposed  that  he  attained  this  equilibrium  by  using  potassium 
stannate  as  an  electrolyte,  but  in  our  opinion  it  is  extremely  doubtful  if  in 
a  solution  of  a  stannate,  the  quadrivalent  tin  ion  is  in  reversible  equilibrium 
with  a  tin  amalgam.  Our  practical  experience  confirms  this  conclusion. 
We  attempted  to  measure  a  cell  with  a  solution  of  sodium  stannate  as  its 
electrolyte,  but  were  unable  to  obtain  anything  approaching  constant 
potentials. 

We  regret  to  state  that  another  fact  also  points  to  the  conclusion  that 
Cady's  work  with  tin  was  questionable.  Roozeboom  and  van  Heteren 
have  shown  that  at  25°  tin  amalgams  containing  from  1.2  to  99  "atom 
per  cent "  of  tin  give  the  same  potential,  there  being  present  two  phases 
of  invariable  composition — a  liquid  phase  containing  1.2  "atom  per  cent" 
tin  and  a  solid  phase  of  99  per  cent  tin.  But  Cady  supposed  he  had  made 
a  tin  amalgam  of  1.73  per  cent  by  weight  or  nearly  3  atom  per  cent,  when 
he  used  potassium  stannate  as  electrolyte  in  the  attempt  to  obtain  the 
potential  of  a  cell  in  which  tin  behaved  as  quadrivalent.  He  calculated 
the  concentration  ratio  on  the  basis  of  his  supposed  percentage."  In 
the  light  of  the  work  of  Roozeboom  and  Van  Heteren  this  work  is  evidently 
faulty,  since  the  strongest  liquid  amalgam  in  the  cell  could  not  have 
exceeded  0.8  per  cent  by  weight  of  tin,  and  the  more  dilute  amalgam 
might  have  been  affected  by  crystals  of  tin  dissolved  on  dilution.  Clearly 
Cady's  work  on  tin  is  without  significance. 

"Jour.  Phys.  Chem.,  2,  551  (1898).  Attention  should  be  called  to  another  serious 
error  in  Cady's  paper,  of  which  due  acknowledgment  was  made.  (Ibid.,  3,  107 
[1899]).  All  this  work  of  Cady's  was  done  under  the  direction  of  W.  D.  Bancroft. 

"  Professor  Cady  has  kindly  looked  up  his  data  in  his  original  note-books,  and 
finds  that  the  mistake  was  not  an  error  of  proof-reading,  but  arose  from  lack  of 
knowledge  of  the  solubility  of  tin  in  mercury. 


30  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

THE  TEMPERATURE  COEFFICIENT  OF  THE  AMALGAM  CELLS. 
Since  all  the  potentials  have  been  measured  at  two  or  three  tempera 
tures,  interest  next  centers  in  the  computation  of  the  temperature  coeffi- 
cients of  the  various  cells.     The  temperature  coefficient  ^  over  a  finite 

range  of  temperature  is  conveniently  divided  by  the  potential  at  o°,  in 
order  to  compare  the  values  obtained  from  the  various  amalgams  with  the 
same  range. 

The  values  of  the  quantity  thus  obtained,—^,,  for  the  thallium,  indium, 

and  tin  amalgams  are  given  in  the  following  table  as  calculated  from  the 
electromotive  forces  already  recorded.  The  change  of  electromotive  force 
between  o°  and  15°  was  almost  always  essentially  identical  with  that 
between  15°  and  30°.  On  account  of  the  comparatively  small  change  of 
electromotive  force,  15°  is  rather  a  small  range  for  this  purpose ;  therefore 
the  whole  range  of  30°  is  given  below  as  the  basis  for  computing  the 
temperature  coefficient. 

The  values  given  in  table  5  are  arranged  in  the  order  of  the  concen- 
tration of  the  most  concentrated  amalgam  in  each  cell.  Thus  the  effect  of 
concentration  upon  the  temperature  coefficient  is  to  be  ascertained  at  a 
glance. 

TABLE  5. — Temperature  Coefficients  of  Electromotive  Force. 


Thallium  amalgams. 

Indium  amalgams. 

Tin  amalgams. 

Per  cent 

Per  cent 

Per  cent 

of 

of 

of 

thallium 

ATT 

indium  in 

ATT 

tin  in 

ATT 

Designa- 

of most 

Designa- 

the more 

Designa- 

the more 

tion  of 

concen- 

^"0^ T 

tion  of 

concen- 

TnA T 

tion  of 

concen- 

Tfp&T 

cell. 

trated 

cell. 

trated 

cell. 

trated 

amalgam 

0°to30°C. 

amalgam 

0°to30°C. 

amalgam 

0°to30°C. 

in  each 

in  each 

in  each 

cell. 

cell. 

cell. 

CI-C2 
C2-C3 

I.8S 
0.52 

0.00319 
0.00350 

EI-E2 

E2-E4* 

1.92 
0.38 

0.00309 
0.00350 

JI-J2 

H2-H3 

0.21 
0.20 

0.00378 
0.00380 

Ai-A2 

0.41 

0.00346 

Fi-F2 

0.32 

0.00360 

J2-J4 

0.06 

0.00378 

C3-C4 

0.23 

0.00355 

F2-F4* 

0.08 

0.00354 

A2-A3 

O.II 

0.00357 

Gi-G2 

0.015 

0.00364 

*  The  cells  E2-E3  and  F2-F3  had  such  small  electromotive  forces  that  the  accu- 
rate measurement  of  the  temperature  coefficients  was  beyond  the  range  of  the 
apparatus.  Therefore  those  cells  were  combined  with  cells  E3-E4  and  F3-F4  re- 
spectively, for  the  present  purpose.  It  should  be  pointed  out  that  the  error  involved 
in  calculating  the  temperature  of  the  indium  cells  is  rather  large,  since  the  poten- 
tials are  small,  the  metal  being  trivalent. 


Although  these  results  are  not  perfectly  regular,  and  show  evidence  of 
experimental  imperfection,  their  general  tendency  is  clear. 


OF   THALLIUM,    INDIUM,    AND   TIN  3! 

The  temperature  coefficients  of  the  thallium  and  indium  amalgams 
exhibit  very  similar  behavior.  The  concentrated  amalgams  give  a  value 
much  lower  than  0.00366  (the  coefficient  of  expansion  of  the  unit  volume 
of  perfect  gas),  but  as  the  dilution  is  increased,  the  coefficient  approaches 
nearer  and  nearer  to  the  ideal  value.  The  most  dilute  indium  cell  measured 
gave  a  value  0.00364,  very  nearly  the  theoretical  coefficient.  This  same 
cell  gave  a  potential  only  0.4  per  cent  different  from  that  demanded  by 
the  formula  of  von  Turin;  thus,  as  the  electromotive  force  approaches 
the  requirement  of  the  gas  law,  the  temperature  coefficient  does  likewise. 

APPLICATION  OF  THE  EQUATION  OF  CADY. 

The  equation  of  Cady  claims  that  the  deviations  from  the  simple  equa- 
tion of  von  Turin  are  due  to  the  heat  of  dilution  of  the  amalgams.*0  On 
comparing  this  equation 


with  the  equation  of  Helmholtz 


it  is  apparent  that  if  the  former  really  held  true,  the  last  terms  of  the 
equations  would  be  identical.  This  was  pointed  out  by  Cady. 

Placing  the  second  members  equal  to  one  another  and  dividing  through 
by  T  we  obtain  the  expression 

R    .     Cm         d-rr  ,    ^ 

VFln7n=dT  U) 

That  is  to  say,  the  temperature  coefficient  should  depend  upon  the  relation 
of  the  concentrations,  not  upon  the  electromotive  force  which  they  hap- 
pen to  exert. 

This  consequence  is  readily  tested  by  the  data  in  hand.     Take  for 

example  the  cell  Ci-C2.  Here  —  =3.516,  and  its  natural  logarithm  is 
1.2574.  Hence  the  first  member  of  the  above  equation  (4)  becomes 

8.316X1.2574  =0.0001082 
1X96,530 

and  the  second  member  becomes 

0.037I34-0-033887  =o.oooio8i 
30.0° 

The  agreement  is  so  striking  that  other  cases  should  be  studied. 
*°Journ.  phys.  Chem.,  2,  551  (1898). 


32  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

Take  for  example  62-63.    Here  —  =3.4104,  and  its  natural  logarithm 

is  1.2268.    Hence  the  first  member  of  the  equation  becomes 
8,316x1^268  =aooo 

1x96,530 
and  the  second  member  becomes 

0.032408-0029303  =0.000^35 
30.0 

Here  the  agreement  is  not  so  good  ;  but,  on  the  other  hand,  it  might  be 
worse.  Another  thallium  amalgam  cell,  Ai-A3,  taken  at  random,  shows 
essentially  the  same  relation,  the  terms  being  as  follows  : 

8.316x1.9808  =0iOOOI700  52.920-47.903  =0.0001670 

96,530  30.0° 

In  the  case  of  indium,  a  somewhat  less  percentage  accuracy  in  fulfilling 
the  requirements  of  the  Cady  equation  is  shown.  For  the  cell  Ei-E2  the 
terms  are  these: 

8.316x1.6082  ^Q  6l  15.786-14.455  =  0.0000444 

3  x  96,530  30.0° 

With  tin,  about  the  same  order  of  agreement  is  to  be  found.  For 
example,  in  the  cell,  Ji-j2,  the  first  member  of  equation  (4)  becomes 


and  the  second  member  becomes 


a  difference  of  about  3  per  cent,  or  about  like  that  found  in  the  case  of 
indium. 

One  conclusion  drawn  from  these  partial  agreements  is  the  same  as 
that  drawn  from  the  case  of  cadmium  studied  by  Richards  and  Forbes, 
namely,  that  the  equation  of  Cady  does  not  contain  an  exact  representation 
of  all  the  influences  producing  electromotive  force.  On  the  other  hand, 
the  new  results  strongly  reinforce  the  hope  expressed  in  the  earlier  paper 
that  this  equation,  although  not  wholly  exact,  is  really  a  step  in  the  right 
direction.  For  it  is  inconceivable  that  all  these  cells,  possessing  very 
different  temperature  coefficients,  one  as  much  as  13  per  cent  different 
from  the  requirement  of  the  gas  law,  should  all  come  within  3  per  cent 
of  the  fulfilment  of  equation  (4),  if  the  equation  were  without  meaning. 

Expressed  in  other  words,  the  meaning  of  the  results  and  mathematical 
considerations  just  detailed  may  be  stated  as  follows  :  The  reason  for  the 
deviation  of  the  actual  electromotive  forces  of  amalgam  cells  from  the 
values  calculated  from  the  concentrations  is  found  to  be  primarily  in  the 
free  energy  of  the  change  of  chemical  affinity  involved  in  the  dilution  of 


OF   THALLIUM,    INDIUM,   AND   TIN  33 

the  amalgams.  The  electromotive  force  may  be  looked  upon  as  being  due 
to  at  least  two  entirely  different  phenomena  superposed  :  one,  the  "  chemi- 
cal free  energy,"  which  manifests  itself  as  heat  on  dilution,  and  the  other 
the  "  osmotic  energy,"  due  to  the  difference  of  concentration  of  the  two 
different  amalgams.  In  these  cells  all  the  free  energy  of  the  essentially 
chemical  part  of  the  change  may  be  supposed  to  appear  as  heat,  because 
the  heat  capacity  of  the  system  is  essentially  unchanged  during  the  reac- 
tion ;  hence  the  system  is  peculiarly  well  adapted  for  tracing  the  mechanism 
of  the  chemical  production  of  electromotive  force.31  This  was  indeed  the 
reason  why  the  whole  investigation  was  undertaken.  The  probable  reasons 
for  the  lack  of  exactness  in  the  application  of  the  equation  of  Cady  will  be 
discussed  in  the  second  half  of  the  monograph,  when  other  results  have 
been  presented. 

APPLICATION  OF  THE  EQUATION  OF  HELMHOLTZ. 

The  importance  of  the  heat  of  dilution  in  the  case  of  amalgam  cells 
leads  one  to  inquire  concerning  its  exact  values  under  the  conditions 
of  the  present  experiments.  These  values  are  most  readily  calculated 
from  the  well-known  equation  of  Helmholtz,  whose  verity  is  undoubted. 
The  only  difficulty  in  the  present  case  lies  in  the  fact  that  the  temperature 
coefficients  were  perforce  determined  over  a  rather  large  range  of  tem- 
perature —  30°  —  on  account  of  their  otherwise  too  insignificant  magni- 
tudes. Moreover,  even  then  their  determination  carries  with  it  by  far  the 
largest  percentage  error  of  any  part  of  the  work.  Fortunately  the  nearly 
if  not  quite  linear  nature  of  the  coefficients  with  these  metallic  cells 
prevents  the  introduction  of  any  considerable  error  from  the  large  range 
needed. 

In  1882,  Helmholtz,  in  a  paper  already  referred  to,  evolved  the  equation 

^F-U=vFT^  (5) 

an  expression  already  given  in  a  somewhat  different  arrangement  as 
equation(i).  According  to  this  expression  the  sum  of  the  heat  of  reaction 
and  the  product  of  the  absolute  temperature  and  the  temperature  coeffi- 
cient of  the  change  of  free  energy  should  equal  the  change  of  free  energy 
itself. 

The  experimental  work  already  described  furnishes  sufficient  data  for 
applying  this  equation  to  the  amalgam  cells  of  thallium,  indium,  and  tin. 

Take,  for  example,  the  thallium  cell  Ci-C2.  Here  ^=0.033897, 
A?r  =0.003237,  AT=3O.oo°,  T=273.O9,  v=i,  and  F= 


"Richards,  Proc.  Am.  Acad.,  38,  293  (1902)  "The  relation  of  changing  heat 
capacity  to  change  of  free  energy,  etc."  This  theorem  has  been  recently  expanded 
mathematically  by  Nernst,  with  the  help  of  an  interesting  assumption  concerning 
the  extrapolation  to  the  absolute  zero. 


34  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID  AMALGAMS 

Then 

ir0vF=     3272.1  joules 

Fv^ ^~T~     2844.4  joules 
Difference  U  =  +  427.7  joules 

Thus  upon  the  dilution  with  mercury  of  an  amalgam  containing  nearly 
two  per  cent  (1.846  per  cent)  by  weight  of  thallium  to  about  treble  its 
volume  (more  exactly,  3.5  fold)  we  should  obtain  428  joules  or  102  small 
calories  for  every  204  grams  of  thallium. 

Again,  in  cell  C2-C3,  TTO= 0.020485,  A*-= 0.002 125,  AT =30.00°, 
7=273.09,  v=  i,  and  F  =  96,530.  Then 

ir0vF  =  1978  joules 

fvTr^  =  1869  joules 

Difference  U—    109  joules 

Turning  now  to  the  indium  amalgams,  we  may  consider  for  example 
the  cell  Ei-E2,  in  which  •*•„  =  0.014455,  ATT  =  0.001331,  A7  =  30.00°, 
7=273.09,  v=3,  F= 96,530. 
Then 

KvF=4i86  joules 

vFT  £ji  =  3509  joules 
Difference  U  =    677 

This  difference,  the  heat  of  dilution,  is  here  much  larger  even  than  in  the 
concentrated  thallium  cell,  because  the  electrochemical  equivalent  of 
indium  is  only  about  one-sixth  as  great  as  that  of  thallium.  In  the  case  of 
a  cell  with  very  dilute  amalgams,  on  the  other  hand,  the  heat  of  dilution  is 
almost  negligible,  as  is  shown  by  the  following  calculation  of  cell  Gi-G2, 
about  a  hundred  times  as  dilute  as  the  previous  example.  There 

wF  =1858  joules 

vFT  ^  =  1862  joules 

Difference  U  =  -  4  joules 

The  agreement  here  is  very  satisfactory,  being  about  0.25  per  cent. 
The  minus  sign  can  hardly  be  significant,  as  the  probable  error  of  the 
measurements  is  as  great  as  4  joules. 

There  now  remains  to  be  considered  only  the  tin  amalgam  cells.  For 
example,  we  have  in  one  cell,  H2-H3:  7r0=o.oio6i4,  A7r=o.ooi2o6, 
AT=30.oo°,  7=273.09°,  v=2,  ^=96,530.  Then 

•KvF=  2284  joules 

vFT^j.=  2353  joules 

Difference  U=—  69  joules 


OF   THALLIUM,    INDIUM,   AND   TIN  35 

Thus  the  dilution  of  the  tin  amalgams  gives  a  small  cooling  effect — a 
conclusion  wholly  in  accord  with  the  deviation  of  its  potential  from  the 
equation  of  von  Turin  and  Meyer.  If  more  concentrated  amalgam  could 
have  been  used,  the  result  would  undoubtedly  have  been  greater. 

If  possible,  it  would  be  well  to  verify  these  values  of  heats  of  dilution 
by  actual  experiment.  Unfortunately,  however,  an  accurate  determination 
of  the  heat  of  dilution  is  only  possible  with  the  more  concentrated  amal- 
gams, and  even  in  these  cases  it  is  difficult.  Five  millionths  of  a  volt  in 
the  potential  of  a  concentration  cell  corresponds  to  the  development  of 
one  joule  during  the  transport  of  an  univalent  gram-atom.  A  mass  of 
amalgam  containing  a  gram-atom  of  thallium  dissolved  in  99  times  its 
weight  of  mercury,  when  diluted  with  an  equal  volume  of  mercury  would 
involve  a  heat  capacity  not  far  from  6000  mayers ;  hence  one  joule  would 
produce  a  temperature  change  of  less  than  0.0002°.  On  account  of  the 
high  inertia  of  mercury,  the  liquids  do  not  mix  easily ;  and  for  the  same 
reason  the  plentiful  stirring  evolves  much  heat.  The  exact  evaluation  of 
the  stirring  correction  is  very  difficult.  Moreover,  the  dilution  must  be 
carried  out  in  an  indifferent  gas  in  order  to  avoid  oxidation  with  its 
attending  heat  effect. 

Nevertheless,  in  spite  of  these  difficulties  the  attempt  was  made  to 
determine  the  heat  of  dilution  in  the  cases  of  the  more  concentrated  amal- 
gams of  thallium  and  indium.  1226  grams  of  a  I  per  cent  thallium  amal- 
gam were  diluted  with  an  equal  bulk  of  mercury  and  found  to  cause  a  rise 
of  0.015°  in  a  calorimetric  system  having  a  heat  capacity  of  431  mayers. 
On  further  diluting  by  an  equal  bulk  of  mercury  the  mixture  resulting 
from  this  first  experiment,  the  increased  system  (having  now  a  heat 
capacity  of  762  mayers)  was  raised  through  only  0.002°.  These  effects 
were  in  the  expected  direction,  but  not  of  the  expected  magnitude. 

The  experiments  were  conducted  in  the  apparatus  of  Richards  and 
Forbes,  in  which  the  mixing  was  conducted  by  a  clock-work  stirrer.  Lack 
of  time  had  prevented  the  proposers  of  this  apparatus  from  testing  it 
thoroughly.  Our  present  experience  indicates  that  the  clock-work  stirring 
was  inadequate,  and  hence  that  an  inadequate  change  of  temperature  must 
have  been  observed  in  all  cases.  Nevertheless,  in  spite  of  the  quantitative 
inadequacy  of  these  results,  they  are  qualitatively  of  value ;  for  they  afford 
experimental  evidence  that  the  conclusions  drawn  from  the  equation  of 
Helmholtz  are  at  least  in  the  right  direction,  and  therefore  that  the  data 
upon  which  the  conclusions  are  based  are  not  seriously  in  error. 

In  the  case  of  indium,  150  grams  of  an  amalgam  containing  1.92  per 
cent  of  indium  was  diluted  with  600  grams  of  mercury  in  a  small  calo- 
rimeter, the  total  heat  capacity  being  157  mayers.  Here,  in  this  smaller 
apparatus,  the  stirring  was  more  effective,  and  the  temperature  rose  0.048°, 


36  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

a  result  more  nearly  in  accord  with  the  expected  value,  but  still  below  its 
full  magnitude.  The  computation  of  the  result  is  not  worth  while,  as  there 
can  be  no  doubt  that  this  experiment,  like  the  others,  has  no  more  than 
qualitative  value. 

The  small  per  cent  of  tin  in  a  tin  amalgam  which  remained  wholly 
liquid  at  o°  corresponds  to  a  heat  of  dilution  which  would  cause  a  change 
of  only  0.002°  in  the  calorimeter  —  -an  amount  too  small  to  be  determined 
within  50  per  cent  by  means  of  our  thermometers.  Hence  an  attempt  to 
carry  out  this  experiment  was  without  object. 

In  view  of  all  these  circumstances,  we  are  inclined  to  agree  with  Carhart 
in  thinking  that  the  electrical  method  of  determining  the  heats  of  dilution 
of  amalgams  is  to  be  preferred  to  the  thermochemical  method. 

It  is  worthy  of  note,  in  this  connection,  that  the  Helmholtz  equation 
shows  at  once  why  the  temperature  coefficient  of  the  electromotive  force 
divided  by  the  electromotive  force  approaches  the  coefficient  of  expansion 
of  a  perfect  gas  as  the  dilution  of  the  amalgam  proceeds.  To  illustrate 
this  relation,  the  equation  may  be  cast  into  a  somewhat  less  familiar  form. 
The  normal  form,  transposed,  is  thus: 


Dividing  through  by  vF-nT,  we  obtain 

^L-  _!_          u 

7rAT~~    T         vF-jrT 

Evidently,  because  U,  the  heat  of  dilution,  diminishes  as  the  dilution  pro- 
ceeds, the  last  term  will  become  smaller  and  smaller.  Finally,  when  the 
heat  of  dilution  becomes  negligible  at  great  dilution,  the  equation  will 

become  simply  ——    =  —  . 


Simultaneously,  the  equation  of  Cady 

_RT1    cm         U 
-Wln~^~^F 
loses  its  last  term,  and  becomes  the  simple  concentration  equation. 

It  is  equally  clear  that  a  positive  heat  of  dilution  (  +  U}  will  cause  the 
potential  to  be  high  and  the  temperature  coefficient  to  be  low.  In  the  case 
of  thallium  and  indium,  this  was  found  actually  to  be  the  case.  On  the 
other  hand,  with  a  negative  heat  of  dilution  (  —  C7)  the  potential  will  be 
low  and  the  temperature  coefficient  high.  This  was  found  to  be  the  case 
with  tin,  and  by  Richards  and  Forbes  with  zinc. 

Thus  the  theory  of  these  cells  seems  to  be  complete,  except  for  the 
quantitative  understanding  of  the  minor  deviations  from  the  equation  of 
Cady.  These  deviations,  which  are  probably  to  be  traced  primarily  to  the 

inaccuracy  of  the  simple  concentration  ratio  £?  as  an  index  of  the  precise 


OF   THALLIUM,    INDIUM,    AND   TIN  37 

osmotic  work  to  be  obtained  from  the  dilution  of  an  amalgam,  may  best 
be  discussed  in  the  light  of  the  further  data  presented  in  the  next  paper. 
Hence  they  will  be  deferred  to  the  conclusion  of  the  monograph. 

In  conclusion,  it  is  a  pleasure  to  express  our  indebtedness  to  the 
Carnegie  Institution  of  Washington  for  the  apparatus  and  materials  used 
in  this  work. 

SUMMARY. 

The  main  points  of  the  present  research  may  be  summarized  as  follows : 

(1)  The   potentials    between    various    liquid    amalgams    of   thallium, 
indium,  and  tin  were  investigated  at  30°  and  o°.    Many  precautions  were 
taken  against  experimental  errors.     The  potentials  of  the  thallium  cells 
are  thought  to  be  reliable  within  o.ooooi  volt;  those  of  the  indium  and 
tin  cells  within  0.000005  volt. 

(2)  Thallium  and  indium  amalgams  gave  potentials  higher  than  those 
calculated  from  the  simple  concentration  law ;  and  tin  amalgams  gave 
potentials  lower  than  those  calculated  from  the  simple  concentration  law. 

(3)  The  temperature  coefficients  of  the  various  cells  have  been  calcu- 
lated and  found  to  approach  the  ideal  value  0.00366  for  a  unit  potential 
as  infinite  dilution  is  approached. 

(4)  The  equation  of  Cady  was  applied  to  the  results,  and  found  to 
afford  a  fairly  accurate  explanation  of  the  deviations  from  the  concentra- 
tion law  in  all  three  cases. 

(5)  The  equation  of  Helmholtz  was  used  for  the  calculation  of  the 
heats  of  dilution,  and  was  found  to  account  for  the  changes  in  the  tempera- 
ture coefficients. 

(6)  It  was  found  impossible  to  obtain  satisfactory  results  with  an  elec- 
trolyte containing  tin  in  a  quadrivalent  condition,  either  as  stannic  chlo- 
ride or  as  sodic  stannate.    In  this  connection  it  was  pointed  out  that  Cady 
must  have  had  a  two-phase  amalgam  in  his  tin  cell,  and  that  his  results 
with  tin  were  illusory. 

(7)  The  density  of  pure  indium  was  determined  and  found  to  be  7.28. 

(8)  The  densities  of  various  liquid  amalgams  of  thallium,  indium,  and 
tin  were  carefully  measured  and  compared  with  the  calculated  values. 

SEPTEMBER  1907  TO  JANUARY  1909. 


209154 


II. 

Electrochemical  Investigation  of  Liquid  Amalgams  of  Zinc, 
Cadmium,  Lead,  Copper,  and  Lithium. 


BY  THEODORE  W.  RICHARDS  AND  R.  N.  GARROD-THOMAS. 


INTRODUCTION. 

Simultaneously  with  the  work  described  in  the  foregoing  paper  a 
similar  investigation  upon  other  metals  was  begun  in  the  laboratory.  The 
parallel  progress  of  these  two  investigations  was  an  assistance  to  each, 
for  not  only  were  the  potentiometer  and  other  apparatus  used  in  common, 
thus  economizing  time  for  each  investigator,  but  also  the  experience  gained 
in  the  one  was  immediately  helpful  in  the  other.  The  object  of  the  work 
to  be  described  was,  of  course,  similar  to  that  of  the  work  just  chronicled, 
namely,  to  extend  as  far  as  possible  the  study  of  liquid  amalgams  in  their 
relation  to  thermodynamical  theory  and  to  the  essential  nature  of  solu- 
tions and  the  galvanic  cell.  The  present  paper  contains,  as  its  title  indi- 
cates, an  experimental  study  of  the  liquid  amalgams  of  zinc,  lead,  copper, 
and  lithium.  It  will  be  seen  that  the  theoretical  discussion  of  these  results 
together  with  those  concerning  cadmium,  thallium,  indium,  and  tin,  already 
described,  furnishes  much  light  upon  these  general  questions  and  the  out- 
come will  be  seen  to  have  justified  the  time  and  trouble  spent  upon  the 
somewhat  exacting  investigation. 

ZINC  AMALGAMS. 

The  energy  changes  involved  in  the  dilution  of  zinc  amalgams  have 
recently  been  studied  in  this  laboratory  by  Richards  and  Forbes."  Zinc 
amalgams  of  different  concentrations,  ranging  from  0.9  per  cent  to  about 
0.015  Per  cent  °f  zinc,  were  connected  by  means  of  an  electrolyte  consist- 
ing of  zinc  sulphate  in  water  ;  and  the  potentials  of  the  resulting  concen- 
tration cells  were  measured,  and  were  compared  with  the  theoretical  poten- 
tial deduced  from  an  equation  derived  from  that  of  von  Turin  :  " 


"Carnegie  Institution  of  Washington,  Publication  No.  56,  p.  36  (1906). 
"Zeit.  phys.  Chem.,  5,  340  (1890). 

39 


4O  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

An  attempt  was  made  also  to  determine  the  heat  which  the  amalgam 
of  concentration  c±  would  evolve  or  absorb  on  dilution  to  concentration  c2 
in  the  case  of  one  cell.  In  this  trial  a  0.9  per  cent  zinc  amalgam  on  dilu- 
tion by  its  own  weight  of  mercury  absorbed  52  joules  per  gram-atom  of 
zinc. 

It  seemed  very  desirable  that  this  thermochemical  result  should  be 
verified  by  the  application  of  the  equation  of  Helmholtz: 


through  the  determination  of  the  temperature  coefficient  of  the  electro- 
motive force.  Lack  of  time  prevented  this  in  the  earlier  work  ;  accord- 
ingly the  present  investigation  was  undertaken. 

The  problem  obviously  involved  simply  the  extension  of  the  work  of 
Richards  and  Forbes  to  two  different  temperatures,  but  the  execution  of 
the  work  was  less  easy  than  had  been  expected.  Since  the  value  of  A?r 
which  would  be  expected  in  the  case  of  the  above  cell  is  very  small,  it  was 
found  necessary  to  make  AT  somewhat  large.  Measurements  were  at 
first  made  at  30°,  15°,  and  o°,  but  the  interval  of  only  15°  is  too  small  to 
allow  of  an  accurate  measurement  of  the  temperature  coefficient,  and  so 
in  the  final  experiments  measurements  were  made  at  30°  and  o°  C.  only. 

Most  of  this  investigation  was  carried  out  in  identically  the  same  way  as 
the  earlier  work,  and  the  densities  of  the  amalgams  were  taken  from  those 
results.  The  methods  of  purification  of  the  zinc,  zinc  sulphate,  and 
mercury,  the  methods  of  preparing  the  amalgams,  of  sealing  them  in 
hydrogen,  and  of  introducing  them  into  the  cell,  and  diluting  them  with 
mercury,  which  had  been  distilled  and  sealed  in  hydrogen,  were  identically 
the  same  in  every  respect. 

The  potentiometer  used  was,  however,  considerably  modified.     If  in  a 

cell  of  a  bivalent  metal  where—  =2,  it  is  desired  to  distinguish  between 
cz 

a  temperature  coefficient  of  0.00366  and  0.00367,  the  potential  of  the  cell 
at  30°  and  o°  must  be  measured  with  an  error  of  not  more  than  0.000002 
volt.  Hence  it  was  clear  that  a  potentiometer  more  sensitive  than  that 
employed  by  Richards  and  Forbes  would  have  to  be  used.  Accordingly, 
much  time  was  spent,  with  the  help  of  J.  Hunt  Wilson,  in  elaborating  a 
suitable  potentiometer.  As  this  instrument  is  described  in  detail  in  the 
foregoing  paper,"  any  further  account  of  it  is  unnecessary  here. 

The  thermostats,  also,  were  the  same  as  those  described  there  ;  they 
could  be  relied  upon  to  keep  at  a  temperature  constant  within  0.01°.  The 
thermometers  were  accurately  standardized  by  means  of  instruments  bear- 
ing the  certificate  of  the  Reichsanstalt. 

M  This  monograph,  pp.  17  to  20. 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM 


ELECTROMOTIVE   FORCE   BETWEEN   ZINC  AMALGAMS. 

The  first  series  of  results  with  zinc  amalgams,  although  not  of  sufficient 
accuracy  to  yield  trustworthy  temperature  coefficients,  are  worth  recording 
as  a  corroboration  of  the  results  obtained  during  the  previous  investigation 
of  Richards  and  Forbes. 

In  the  first  case  the  most  concentrated  amalgam  contained  0.90  per  cent 
of  zinc.  It  was  placed  undiluted  in  the  first  cup  of  the  multiple  cell 
described  in  the  foregoing  paper,"  was  diluted  with  mercury  in  the  third 
and  fourth  cups,  and  finally  the  parent  amalgam  was  again  put  undiluted 
in  the  remaining  second  cup,  in  order  to  be  sure  that  no  change  had  taken 
place  in  the  amalgam  during  the  filling  of  the  cell,  and  also  that  the 
amalgam  had  been  in  the  first  place  thoroughly  mixed.  This  precaution 
was  usually  taken  in  the  subsequent  work  also,  but  only  in  one  case, 
mentioned  later,  was  a  difference  greater  than  0.000002  volt  ever  found 
between  the  first  and  the  last  portions  of  amalgam.  As  is  shown  below, 
the  maximum  difference  in  the  present  case  was  only  one  millionth  of  one 
volt. 

In  addition  to  this  series  of  measurements,  another  was  made  upon  three 
more  dilute  amalgams,  in  order  to  show  the  increasingly  near  approach 
of  the  potential  to  the  gas  law.  Table  6  gives  both  series  of  measure- 
ments at  30°.  The  details  of  dilution,  etc.,  need  not  be  given  as  regards 
these  preliminary  results.  The  theoretical  potential  given  below  is  calcu- 
lated according  to  the  simple  concentration  equation. 

TABLE  6. — Preliminary  Electrical  Measurement  of  Zinc  Amalgams. 


Designation 
of  cup 

Approximate 
per  cent  of 

Exact 
value  of 

Electromotive  force,  in  millivolts,  be- 
tween each  pair  of  cups.    3(PC. 

amalgam. 

amalgams. 

108  g 

Observed. 

Theoretical. 

Difference. 

Ki  

0.000, 

f  •' 

0.0000 

0.001 

0.000 

O.OOI 

K2  

0.000 

f  •' 

0.37045 

10.175 

11.129 

0.954 

K3  

0.384 

I" 

0.21459 

6.123 

6.446 

0.323 

K4  

0.234' 

Li  

0.100  i 

\" 

0.44404 

13.262 

13.341 

0.079 

L2  

0.036  I 

•• 

0.26303 

7.828 

7-903 

0.075 

L3  

0.020  ' 

'This  monograph,  p.  15. 


ELECTROCHEMICAL   INVESTIGATION    OF   LIQUID   AMALGAMS 


These  results  confirm  wholly  the  work  of  Richards  and  Forbes,  carried 
out  at  23°,  showing  that  cells  of  zinc  amalgams  give  a  much  lower  electro- 
motive force  than  that  required  by  the  concentration  law.  The  quantita- 
tive agreement  of  the  two  series  of  results  is  shown  in  the  accompanying 
diagram  (fig.  9),  where  the  points  surrounded  by  single  circles  are  the 
points  found  by  the  earlier  work,  and  those  surrounded  by  double  circles 
the  present  data.  This  curve  is  drawn  on  the  same  scale  as  that  used  in 
the  other  similar  curves  in  this  monograph. 

The  cells  were  measured  also  at  15°  and  o°.  In  no  case  did  the  poten- 
tial between  cups  I  and  2  exceed  o.oooooi  volt.  At  30°  the  other  measure- 
ments also  were  sufficiently  concordant  and  convincing.  At  o°  the  more 
dilute  amalgams  gave  less  consistent  results,  and  evidently  were  not  so 


logE        Iog4         logS        log  16        log  32       log  64       logJ28      log  256 
Fig.  9.  The  Deviations  of  the  Electromotive  Force  of  Zinc  Amalgams. 

Deviations   from   the   expression    w  =  ~  in  c±    are  plotted   in   millivolts   as   ordinates, 

the  logarithms  of  the  concentration  ratios  as  abscissae.  The  most  concen- 
trated amalgam  contained  0.9  per  cent  by  weight  of  zinc  and  99.1  per  cent 
by  weight  of  mercury.  A  horizontal  line  on  the  diagram  would  indicate 
complete  fulfilment  of  the  concentration  law.  This  curve  is  almost  if  not 
quite  independent  of  temperature,  at  least  between  o°  and  30°.  Single  circles 
depict  points  found  by  Richards  and  Forbes;  double  circles  depict  points 
found  by  the  present  investigation. 

trustworthy.  As  the  technique  and  accordingly  the  consistency  of  the 
results  were  both  greatly  improved  later,  these  early  measurements  need 
not  be  given  in  detail.  It  is  enough  to  say  that  there  was  undoubted 
evidence  of  the  truth  of  the  prediction  of  Richards  and  Forbes  that  the 
temperature  coefficient  is  greater  than  0.00366,  demanded  by  the  gas  law. 
Moreover,  it  was  clear  that  the  value  approached  more  and  more  nearly 
that  required  by  the  gas  law  as  the  dilution  became  greater. 


OF   ZINC,    CADMIUM,   LEAD,    COPPER,   AND   LITHIUM  43 

DETERMINATION   OF  THE  TEMPERATURE  COEFFICIENTS   OF  CELLS 
CONTAINING   ZINC  AMALGAMS. 

The  previously  described  measurements  had  all  been  made  with  the 
potentiometer  in  its  original  less  complete  condition.  For  further  more 
accurate  experiments,  the  potentiometer  was  modified  with  a  view  of 
eliminating  all  thermoelectric  currents,  as  has  been  already  described." 
The  air  in  the  case  containing  the  potentiometer  was  stirred  by  means  of 
a  fan,  worked  by  an  electric  motor  outside  the  case,  so  that  the  tempera- 
ture inside  was  sensibly  uniform.  It  was  also  arranged  that  all  final 
adjustments  on  the  potentiometer  could  be  made  from  outside  the  case, 
thus  avoiding  all  danger  of  thermal  effects  due  to  heating  by  the  warmth 
of  the  operator.  Moreover,  the  connections  with  the  cell  were  made  so 
as  to  avoid  thermoelectric  effects ;  contact  was  made  between  copper  and 
mercury  well  under  the  surface  of  the  thermostat  and  inside  the  cell,  so 
that  all  unequal  heating  of  junctions  of  dissimilar  metals  was  avoided. 

A  series  of  test  experiments  with  this  improved  potentiometer  showed 
that  although  thermal  currents  had  been  completely  eliminated,  so  that  the 
potentials  could  be  read  to  even  less  than  o.oooooi  volt,  nevertheless,  the 
amalgam  cells  themselves  were  not  constant  to  this  same  degree.  It  was 
thought  that  the  irregularities  might  be  due  to  the  formation  of  a  basic 
salt  by  the  action  between  the  amalgam  and  water.  To  test  this,  in  one 
case  the  electrolyte  was  made  slightly  acid  (about  0.02  N.  with  H2SO4) , 
but  no  effect  was  observable,  and  hence  in  the  final  experiments  neutral 
electrolyte  was  again  used. 

In  all  the  measurements  thus  far  recorded  the  potential  at  29.96°  was 
first  measured,  and  then  the  potential  at  o°,  and  finally  the  readings 
repeated  at  29.96°  and  at  o°  again.  It  was  always  found  that  the  reading 
at  29.96°  remained  throughout  constant  to  about  0.000005  vo^,  while  the 
value  at  o°  showed  much  greater  change,  sometimes  even  as  much  as 
0.000030  volt.  If  the  cell  at  29.96°  was  shaken,  the  values  were  only 
temporarily  altered,  while  at  o°  this  treatment  caused  a  more  permanent 
change,  which  did  not  completely  vanish  even  if  the  cell  was  heated  to 
29.96°,  and  cooled  to  o°  again. 

Being  unable  to  eliminate  the  difficulty,  we  sought  to  arrange  the  experi- 
ments in  such  a  way  as  to  minimize  its  influence.  In  the  final  set  of  read- 
ings to  be  recorded,  the  amalgams  and  electrolyte  were  cooled  before  using, 
and  were  put  into  the  cell  as  cold  as  possible.  The  readings  at  o°  were 
first  taken  and  then  the  readings  at  the  higher  temperature.  Finally  the 
cell  was  cooled  to  o°  and  measured  again.  The  first  readings  at  o°  and 
the  readings  at  30°  were  constant,  even  if  the  cell  was  shaken,  but  the 
second  series  at  o°  showed  after  a  time  the  former  irregularities. 

"This  monograph,  pp.  17-20. 


44 


ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID  AMALGAMS 


In  order  to  make  these  results  as  definite  as  possible,  it  was  decided  to 
carry  out  two  sets  of  experiments  simultaneously,  the  two  cells  containing 
the  same  amalgams.  To  effect  this,  the  usual  method  of  diluting  a 
"parent"  amalgam  in  the  cell  was,  of  course,  impracticable,  and  four 
separate  amalgams  had  to  be  made  and  sealed  in  the  pipettes.  The  con- 
centration of  these  amalgams  was  known  to  within  about  0.5  per  cent — 
a  degree  of  accuracy,  which,  although  not  sufficient  to  admit  of  the  theo- 
retical potentials  being  calculated  with  the  utmost  precision,  was  ample 
for  finding  the  temperature  coefficients  with  great  exactness. 

The  cells  were  filled  as  in  table  7. 

TABLE  7. 


Cup. 

Per  cent  of  zinc. 

Cell  M. 

Cell  N. 

2 

3 
4 

O.QI3 
0.296 
0.0998 
0.0302 

0.913 
0.303 
0.0098 
0.0302 

The  cells  were  then  put  into  the  o°  bath,  and  their  potentials  measured 
at  two  intervals  of  about  an  hour,  the  cell  being  shaken  between.  The 
greatest  change  in  potential  during  this  treatment  was  0.000004  v°lt-  Cell 
N  was  then  put  in  the  30°  bath,  and  each  pair  of  amalgams  was  put  in 
opposite  to  the  similar  pair  in  cell  M  at  o°,  and  hence  a  direct  measure- 
ment of  the  temperature  change  was  obtained.  Cell  M  was  then  put  in 
the  30°  bath,  and  the  potential  of  both  cell  M  and  cell  N  determined  at 
30°  ;  finally,  N  was  once  more  packed  in  ice,  but  after  two  readings  had 
been  taken,  the  familiar  irregularities  at  o°  became  too  great  for  further 
accurate  work. 

A  slight  mischance  prevented  the  complete  fulfilment  of  the  program, 
but  although  this  mischance  complicated  affairs,  it  did  not  interfere  with 
the  significance  of  the  results  for  the  present  purpose.  Probably  because 
of  insufficient  mixing  in  the  bulb  before  the  stem  was  filled,  the  amalgam 
in  cup  M2  was  found  to  be  slightly  less  concentrated  than  in  N2.  This 
prevented  the  direct  comparison  of  these  two  cups,  but  did  not  affect  the 
results  from  each  separately.  The  concentrations  of  the  amalgams  in  these 
two  cups,  as  given  above,  were  calculated  from  their  potentials  in  con- 
nection with  the  others,  by  the  method  given  at  the  very  end  of  this  paper. 
All  the  other  cups  were  perfectly  comparable,  as  was  shown  by  the  precise 
equality  of  each  pair,  both  at  o°  and  at  30°. 

All  the  figures  in  table  8,  except  the  last  two  columns,  represent  the 
actual  readings  of  the  potentiometer.  The  last  two  columns  are  obtained 
by  difference  from  the  appropriate  preceding  columns. 


OF  ZINC,    CADMIUM,    LEAD,    COPPER,   AND   LITHIUM 

TABLE  8. 


45 


Cell. 

MatO°. 

NatO°. 

Nao-Mo- 

Mat  30°. 

Nat  30°. 

M.O-NO. 

M»-MO. 

NK-NO. 

1-2 

1-3 

II.8I3 
24.236 

II-S30 
24.241 

"2'.79l" 

13-211 
27.033 

12.897 
27.029 

2.795 

1.398 
2.793 

1.367 

2.788 

1-4 

38.196 

38.196 

4.327 

42.527 

42.525 

4-330 

4-333 

4.329 

2-3 

12.427 

12.714 

13  831 

14   138 

I   404 

2-4 

26.393 

26.669 

29  .  33  i 

29  637 

2  0^8 

2-968 

3-4 

I3-960 

1-544 

15.507 

15.506 

1-543 

1-545 

1-544 

Thus  for  cups  1-3  there  are  four  results  for  ATT  to  be  taken  directly 
from  the  table,  and  three  more  by  subtracting  the  values  for  the  cups  3-4 
from  those  for  the  cups  1-4.  There  are  also  four  values  for  the  value  of 
ir  for  1-3  at  o° — two  given  in  the  table,  and  two  obtained  by  subtracting 
the  values  for  3-4  from  those  for  1-4.  These  are  recorded  below  in 
table  9,  in  order  to  give  some  idea  of  the  accuracy  of  the  work. 

TABLE  9. 
[Cell  Mi-M3  (or  Ni-Na)]. 


TTO  in  millivolts. 

AT  (o°  to  29.%°),  in  millirolts. 

24.236 
24.241 
24-234 
24.236 

2.791 

2.795 
2.793 
2.788 

Average                      24  237 

•7°3 
2   788 

2.785 

Average                        2  799 

"Probable  error"..  0.0008 

"Probable  error".  ..  o.ooi 

Thus  this  cell  with  its  amalgams  containing  about  0.0913  and  o.ioo 
per  cent  of  zinc,  respectively,  gave  a  potential  of  0.024237  volt  ±0.0000008 
at  o°,  and  changed  its  potential  by  0.002799  volt  ±0.000001  on  being 

raised  to  29.96°.    The  value  for  -^-  is  therefore  0.003855  instead  of  the 

value  0.00366  shown  by  the  increase  in  pressure  of  a  nearly  perfect  gas — 
the  standard  upon  which  our  temperature  scale  rests. 

In  the  same  way,  seven  results  for  cell  1-4  give  on  the  average 
ATT =0.004332  volt  ±0.000001 ;  and  for  cell  3-4,  seven  similar  results  give 
ATT =o.ooi  541  volt  ±o.oooooi.  From  these  results,  as  well  as  from  the 
figures  given  in  the  table  for  the  other  combinations,  the  corresponding 
values  for  the  temperature  coefficients  may  be  readily  computed,  it  being 
borne  in  mind  that  wherever  cup  2  is  concerned,  the  cells  M  and  N  must 


46  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

be  calculated  separately.  When  thus  treated  the  final  results  from  the 
two  are  essentially  identical,  and  may  be  averaged  together.  As  the 
details  may  be  worked  out  from  the  data,  by  anyone  wishing  to  verify  the 
results,  further  space  need  not  be  wasted  by  their  minute  presentation. 

It  is  enough  to  present  the  final  table  of  values  for  the  function  —  -J_ . 


Cup    1-2 0.00397 

1-3 0.003855 

1-4 0.003794 


Cup  2-3 0.00375 

2-4 0.003715 

3-4 0.003685 


Thus  it  is  clear  that  in  the  case  of  zinc  amalgams,  as  in  all  other  cases 
thus  far  studied,  the  temperature  coefficient  of  the  electromotive  cell 
becomes  nearer  and  nearer  the  limiting  value  as  the  dilution  proceeds. 
In  the  most  dilute  cell  measured,  whose  two  amalgams  contained  respec- 
tively about  o.io  and  0.03  per  cent  of  zinc,  the  value  of  the  temperature 
coefficient  had  come  within  0.7  per  cent  of  the  requirement  of  the  gas  law. 
The  significance  of  these  results  as  regards  the  theory  of  the  galvanic 
cell  will  be  discussed  in  a  later  section,  after  the  facts  concerning  other 
cells  have  been  presented. 

It  will  be  observed  that  the  first  value  given  for  the  temperature  coeffi- 
cient exceeds  the  ideal  value  by  as  much  as  8.5  per  cent.  This  high  value 
for  the  temperature  coefficient,  which  appears  wherever  the  most  con- 
centrated amalgam  was  concerned,  might  possibly  be  due  to  the  crystal- 
lization of  zinc  at  o°.  That  this,  however,  was  not  the  case  seems  almost 
certain  from  the  regularity  of  the  results  obtained,  and  from  the  fact  that 
the  temperature  coefficient  between  15°  and  o°,  and  between  30°  and  o° 
for  even  a  stronger  amalgam  than  was  here  used,  were  nearly  the  same. 

The  point  was,  however,  also  experimentally  investigated  in  the  fol- 
lowing manner.  Both  the  limbs  of  an  H  tube  were  filled  with  a  0.91  per 
cent  zinc  amalgam,  and  the  potential  between  them  at  o°  was  measured 
and  found  to  be  almost  zero.  Then  a  small  quantity  of  pasty  zinc  amalgam 
was  added  to  one  limb,  and  a  large  and  permanent  potential  was  produced 
in  the  direction  indicated  by  theory.  In  another  similar  cell,  one  of  the 
limbs  was  very  slightly  diluted  with  mercury  and  again  a  permanent  poten- 
tial, in  the  direction  foretold  by  theory,  was  observed.  These  facts  could 
not  be  explained  if  the  parent  amalgam  had  crystallized  out  at  o°,  but  are 
precisely  what  would  be  expected  from  an  unsaturated  amalgam. 

Control  experiments  were  made  in  which  an  amalgam  known  to  be  more 
than  saturated  replaced  the  0.91  per  cent  amalgam  in  the  above  experi- 
ments. On  the  dilution  and  on  the  concentration  of  one  of  the  sides  of 
the  cell  no  permanent  potential  greater  than  o.ooooi  volt  was  obtained, 
showing  in  this  case  that  the  presence  of  the  solid  phase  caused  the  effec- 
tive concentration  of  the  amalgam  to  become  constant. 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,   AND   LITHIUM 


47 


LEAD  AMALGAMS. 

In  order  to  generalize  concerning  facts  of  any  kind,  it  is  desirable  to 
obtain  as  wide  a  variety  of  data  as  possible.  Hence  it  was  decided  to 
investigate  lead  amalgams  in  the  same  manner.  Previous  work  on  the 
subject  had  been  done  by  G.  Meyer,"  and  by  Spencer,"  but  no  data  of 
sufficient  accuracy  had  been  published.  The  investigation  was  carried 
out  in  a  manner  exactly  similar  to  the  above-described  work,  hence 
details  of  manipulation  will  not  be  described  again. 

Commercial  "  C.  P."  lead  acetate  was  found  to  contain  traces  of  iron, 
but  after  one  recrystallization  with  centrifugal  filtration  this  impurity  was 
eliminated,  and  after  two  more  such  crystallizations  the  lead  acetate  was 
considered  sufficiently  pure  to  be  used  as  the  source  of  the  metal,  as  well 
as  for  the  electrolyte. 

The  metallic  lead  used  was  prepared  by  the  electrolysis  of  the  acetate 
solution.  The  crystals  of  the  metal  thus  obtained  were  carefully  washed, 
and  were  then  fused  in  porcelain  boats  in  an  atmosphere  of  hydrogen,  and 
the  lead  thus  obtained  was  used  to  make  the  amalgams.  The  electrolyte 
was  prepared  by  taking  a  solution  of  the  acetate,  saturated  at  o°,  and 
diluting  with  about  one-tenth  its  volume  of  half  normal  "  chemically  pure  " 
acetic  acid.  In  this  way  the  formation  of  basic  salts  was  prevented,  and  a 
perfectly  clear  electrolyte  was  obtained.  This  solution  was,  as  usual, 
boiled  in  a  partial  vacuum  in  an  atmosphere  of  hydrogen,  and  sealed  in  a 
pipette,  also  in  hydrogen. 

The  amalgams  were  made  by  adding  a  weighed  amount  of  lead  to  a 
weighed  amount  of  hydrogen-distilled  mercury,  a  little  very  dilute  acetic 
acid  being  present  to  cover  the  metals  and  prevent  oxidation ;  for  the 
amalgam  oxidizes  very  rapidly  in  air.  The  acetic  acid  was  then  analyzed, 
and  was  found  to  contain  neither  lead,  nor  iron  from  the  steel  knife  used 
to  cut  the  lead.  The  amalgams  were  then  sealed  in  hydrogen  in  the 
before-described  apparatus. 

TABLE  10. 


Concentration 
of  amalgam 
(per  cent). 

Weight  of  pycnometer  full  of- 

Density 

atao°c. 

Amalgam. 

Mercury. 

1.02 

0.684 

0.397 

0 

48.9587 
35-073 
35-079 

48.9922 
35.092 
35.092 
35.092 

13.536 
13-539 
13.541 
13-545 

Zeit.  phys.  Chem.,  7,  477. 


"Zeitschr.  f.  Electrochem.,  11,  681. 


ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 


A  series  of  density  experiments  of  lead  amalgams  was  carried  out  at 
20°,  and  is  recorded  in  table  10,  but  the  necessary  correction  is  insignifi- 
cant in  this  case,  because  the  density  of  lead  is  so  nearly  that  of  mercury. 
The  densities  were  determined  by  the  use  of  an  ordinary  Ostwald  pyc- 
nometer ;  the  only  unusual  precaution  taken  was  to  displace  the  air  in  the 
pycnometer  by  carbon  dioxide.  On  this  account  very  little  oxidation  took 
place  when  the  amalgams  were  drawn  into  the  tube. 

These  results  are  plotted  in  fig.  10.  The  imaginary  density,  supposing 
no  contraction  to  have  happened,  is  given  by  the  dotted  line.  For  a  I  per 
cent  amalgam  this  is  13.524  instead  of  the  actually  observed  value  13.536. 
Thus  as  a  matter  of  fact  a  slight  contraction  occurs  on  amalgamation. 


13.53 


13.54 


13.55 


0.2 


0.6 


0.8 


1.0  percent 


Fig.   10.  Densities  of  Lead  Amalgams  at  20°. 


Densities  are  plotted  as  ordinates,  per  cents  by  weight  of  lead  in  amalgams  as  abscissae. 
The  dotted  line  indicates  the  imaginary  theoretical  values. 

The  electrical  measurement  of  similar  amalgams  was  now  undertaken. 
The  most  concentrated  amalgam  of  lead  used  for  the  purpose  contained, 
as  before,  1.02  per  cent  of  this  metal  by  weight.  Some  of  this  was  placed 
in  the  cup  labeled  Pi.  Into  cups  P2,  P3,  and  P4  were  placed  respectively 
12.684,  I2-6o3>  and  10.946  grams  of  this  amalgam,  diluted  with  19.358, 
58.96,  and  108.86  grams  of  mercury  respectively.  The  second  series 
began  about  where  this  left  off,  with  a  freshly  prepared  amalgam  contain- 
ing 0.0994  per  cent  of  lead.  Cup  Qi  contained  this  alone,  while  cup  Q2 
contained  14.308  grams  of  it  diluted  with  74.628  grams  of  mercury.  The 
least  concentrated  amalgam  of  all,  that  contained  in  Q3,  was  made  by 
diluting  8.429  grams  of  material  like  that  in  Qi  with  115.72  grams  of 
mercury.  The  electrical  measurement  with  these  two  series  of  cells  is 
given  in  table  n. 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM 
TABLE  n. — Electrical  Measurement  of  Lead  Amalgams. 


49 


Designation 
of  cup 
containing 
amalgam. 

Approxi- 
mate 
per  cent  of 
lead  in 

amalgams. 

Exact 
value  of 
.        Cm 

Electromotive  force  between  each  pair  of  cups,  in  millivolts. 

0°C. 

29.96°C. 

10B*. 

Observed. 

Theo- 
retical. 

Differ- 
ence. 

Observed. 

Theo- 
retical. 

Differ- 
ence. 

Pi  
P2  .  . 

,« 

0.404     j 
0.180     | 
0.0932  ' 
0.0994, 

0.0160  | 
0.0068' 

0.4023 
0.3SI7 
0.2850 

0-7935 
0-3747 

8.960 

8.839 
7.422 

21.303 
10.077 

10.895 
9.525 
7.719 

21.489 
10.149 

1-935 
0.686 
0.297 

0.186 
0.072 

10.135 
9.841 
8.270 

23.680 
11.186 

12.092 
10.509 
8.564 

23.848 
11.262 

1.957 
0.728 
0.294 

0.168 

0.076 

P3  ..  . 

P4  
Ql 

Q2 

Q3  

The  last  column  in  table  n  shows  the  great  deviation  of  the  strongest 
amalgams  from  the  simple  equation 

RT      c« 

vF   ^   Cn 

and  indicates,  as  usual,  that  this  deviation  approaches  zero  as  the  dilution 
proceeds  in  the  usual  fashion.     The  fact  becomes  yet  clearer  when  the 
results  are  plotted  as  the  other  metals  have  been.    Fig.  1 1  gives  this  curve, 
drawn  on  the  same  scale  as  those  previously  given. 
0 


log  a        Iog4         Iog8         log  16          Iog32        log  64     loglZB 
Fig.  11.  The  Deviations  of  the  Electromotive  Force  of  Lead  Amalgams. 


log,256 


Deviations    from    the    expression  n  =  -^p  In  •—•  are    plotted    in    millivolts    as    ordinates, 


the  logarithms  of  the  concentration  ratios  as  abscissas.  The  most  concentrated 
amalgam  contained  1.02  per  cent  by  weight  of  lead  and  98.98  per  cent  by 
weight  of  mercury.  A  horizontal  line  on  the  diagram  would  indicate  com- 
plete fulfilment  of  the  concentration  law.  This  curve  is  almost  if  not  quite 
independent  of  temperature,  at  least  between  o°  and  30°. 


ELECTROCHEMICAL   INVESTIGATION    OF   LIQUID   AMALGAMS 


The  temperature-coefficient  functions 


ATT 


of  these  cells,  calculated  in 


the  usual  way  from  the  figures  given  in  table  n,  are  as  follows: 


Cell  Pi-P2 0.00437 

P2-P3 0.003805 

P3-P4 0.00381 


Cell  Qi-Cj2 0.00376 

CJ2-Q3 0.003677 


The  first  value  is  much  higher  even  than  that  for  zinc.  Here  again  as 
usual,  the  figures  rapidly  approach  the  limiting  value  0.00366  as  the 
dilution  proceeds,  although  the  coefficient  for  cell  Pi-P2  containing  the 
most  concentrated  amalgams  is  16  per  cent  in  excess  of  this  figure. 

The  theoretical  significance  of  these  results  will  be  considered  later,  in 
connection  with  all  the  other  results.  The  possibility  that  the  high  tem- 
perature coefficient  of  the  most  concentrated  amalgam  cell  might  be  due 
to  the  crystallization  of  the  most  concentrated  amalgam  at  the  lower 
temperature  was  considered,  and  was  experimentally  investigated  in  an 
exactly  similar  manner  to  that  used  in  the  case  of  the  zinc  amalgams. 
An  amalgam  containing  1.03  per  cent  of  lead  was  placed  in  an  H  cell  and 
one  side  was  in  one  case  diluted  and  in  the  other  concentrated,  and  in 
both  cases  a  permanent  potential,  in  the  direction  indicated  by  theory, 
was  obtained,  the  measurements  of  course  being  made  at  o°  C.  Control 
experiments,  using  a  saturated  amalgam  with  excess  of  lead,  showed  no 
potential  on  adding  either  mercury  or  lead  to  one  side  of  the  cell. 

These  results  seem  to  show  clearly  that  the  most  concentrated  amalgam 
used,  i.  e.,  1.02  per  cent,- is  less  than  saturated  at  o°. 

At  this  point  the  potentiometer  was  recalibrated,  but  no  change  as  great 
as  o.oi  ohm  was  found  in  any  of  the  resistance,  and  hence,  as  before,  cor- 
rections were  unnecessary. 


COPPER  AMALGAM. 

Seeking  all  the  light  available  upon  this  type  of  cell,  the  investigators 
next  turned  to  the  metal  copper.  Copper  amalgams  have  been  examined 
in  this  connection  by  Meyer  and  by  Spencer.  Meyer  made  an  amalgam, 
by  electrolysis,  intended  to  contain  0.217  per  cent  of  copper.  This  amal- 
gam he  dried  by  filter-paper  and  standing  in  a  desiccator,  and  then  diluted 
portions  of  it.  Table  12  gives  his  results,  the  concentration  being  ex- 

TABLE  12. — Potentials  of  Copper  Amalgams  measured  by  Meyer. 


/. 

a. 

C2. 

Electromotive 
(millivolts). 

Mol.  wt.,  calc. 

17.3 

20.8 

0.03874 
0.04472 

0.009587 
0.016645 

I8.I5 
12.4 

63.3 
63.7 

OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM  51 

pressed  in  percentage,  and  not  in  parts  per  unit  of  mercury,  as  it  is  in  the 
original  paper." 

The  results  obtained  by  Spencer  were  not  so  consistent  with  theory, 
but,  as  will  be  seen,  are  more  like  our  own  experience.  He  found  great 
difficulty  in  getting  constant  readings  of  potential.  His  results  are  given 
in  table  13 ;  it  will  be  observed  that  he  used  far  more  dilute  amalgams. 

TABLE  13. — Potentials  of  Copper  Amalgams  measured  by  Spencer. 


No.  of 
cell. 

Per  cent  of  copper. 

Electromotive  force. 

| 
Cl. 

Observed. 

Theoretical. 

I. 
II. 

III. 

0.0003193 
0.001938 
0.005399 

0.001938 
0.005399 
0.007205 

26.8 

6.4 

20.9 

IO.I 

8.8 

It  will  be  noticed  that  at  first  the  actual  potential  is  larger  than  theory, 
and  afterwards  smaller.  The  reason  will  soon  become  clear. 

The  next  step  of  the  present  research  was  to  repeat  these  experiments 
in  order  to  discover  the  difficulty.  Commercial  "  C.  P."  copper  sulphate 
was  carefully  recrystallized  three  times  with  centrifugal  filtration,  and  the 
resulting  copper  salt  was  used  in  the  experiments.  A  copper  amalgam 
was  then  made  by  electrolysis,  using  mercury  as  the  cathode,  the  amount 
of  copper  deposited  being  estimated  by  means  of  a  silver  coulometer  in 
series.  The  amalgam  was  found  to  contain  0.2311  per  cent  of  copper.  On 
drawing  this  amalgam  into  the  pipette,  preparatory  to  its  being  sealed  in 
hydrogen,  a  pasty  residue  was  left  which  would  not  enter  the  fine  tip  of 
the  pipette.  Hence  it  was  clear  that  the  above  amalgam  was  not  a  solu- 
tion, but  rather  a  suspension  of  copper  or  of  some  copper-mercury  com- 
pound in  mercury.  The  amalgam  which  had  been  drawn  into  the  pipette 
was  used  to  fill  a  cell  in  the  ordinary  manner. 

This  cell  proved  two  important  points :  first  that  neutral  copper  sulphate 
could  not  be  used  as  electrolyte,  because  the  amalgam  acted  on  it,  giving 
Cu2O ;  and  secondly,  that  a  very  dilute  amalgam,  made  by  diluting  the 
original  sixteen  times,  gave  only  an  exceedingly  small  potential  with  the 
original  amalgam.  Thus  it  appeared  that  the  diluted  amalgam  was  still 
saturated  and  there  could  be  no  doubt  that  crystals  of  the  solid  had  not 
all  been  left  behind  in  the  pasty  mass  mentioned  above. 

It  then  became  necessary  to  find  the  solubility  of  copper  in  mercury. 
Saturated  solutions  of  copper  in  mercury  were  made  either  by  allowing 
amalgamated  copper  wire  to  stand  in  mercury  for  a  week,  or  by  carefully 
filtering  a  partially  solid  amalgam,  prepared  electrolytically,  several  times 
through  leather. 


'  Zeit.  phys.  Chem.,  7,  477. 


ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 


The  saturated  amalgam  was  then  weighed,  and  the  mercury  driven  off, 
at  first  by  distillation  in  hydrogen,  and  the  last  traces  by  heating  to  a  red 
heat  in  a  crucible.  The  cupric  oxide  left  was  then  either  directly  weighed, 
or  it  was  dissolved  in  nitric  acid,  neutralized  with  ammonia  and  the  con- 
centration of  the  solution  approximately  estimated  by  colorimetric  com- 
parison with  the  color  of  a  standard  solution  of  ammoniacal  cupric  nitrate. 
The  results  are  given  in  table  14. 

TABLE  14. — Solubility  of  Copper  in  Mercury  at  20". 


Method  of  preparation. 

Weight  of 
amalgam 
(grams). 

Method  of  analysis. 

Weight  of 
<££ 

Solubility 
(percent). 

Copper  +  mercury 

41   I 

Colorimetric  

0.08 

o  0024 

Do 

885 

Direct  weighing 

2  OO 

o  0023 

Electrolysis  +  filtration 

30  o 

Colorimetric 

o  60 

O  O02O 

Do 

mo  o 

Direct  weighing 

4  05 

o  0027 

o  002^"? 

Thus  the  solubility  of  copper  in  mercury  at  room  temperature  seems  to 
be  very  small  indeed,  about  0.0024  per  cent,  or  about  I  milligram  in  40 
grams  of  mercury.  This  agrees  well  with  the  observations  of  Sir  W. 
Ramsay,40  but  is  somewhat  higher  than  a  result  of  Gouy.*1 

It  was  then  decided  to  measure  electrically  a  series  in  which  the  start- 
ing point  should  be  undoubtedly  a  real  solution.  An  amalgam  containing 
about  i  per  cent  of  copper  was  made  electrolytically.  It  was  then  filtered 
three  times  through  leather,  the  last  filtration  leaving  no  solid  residue. 
153  grams  of  this  amalgam  were  then  diluted  with  26  grams  of  mercury 
in  order  to  make  quite  certain  that  no  solid  was  present.  This  amalgam 
was  bottled  in  the  usual  way.  It  was  estimated  to  contain  about  0.0020 
per  cent  of  copper. 

TABLE  15. 


Cell. 

Electromotive  force,  in  millivolts. 

Observed. 

Theoretical. 

After  i  hour. 

24  hours. 

48  hours. 

72  hours. 

1-2 
1-3 
1-4 

15.20 
31-6 

43-8 

14.70 
32.0 
40.7 

9.1 

I7"i 

21.6 

5-4 
10.8 
13-8 

H-53 
27.38 
34.83 

*°Journ.  Chem.  Soc.,  1889,  Trans,  n,  532. 

41  Gouy,  Ann.  der  Phys.  Beiblatter,  19,  758.     He  found  q.ooi  per  cent  of  copper, 
1.8  per  cent  of  zinc,  and  1.3  of  lead  in  their  respective  liquid  amalgams. 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM 


53 


The  cell  was  then  filled,  using  this  amalgam  in  cup  i,  diluting  it  in  the 
three  other  cups  of  the  multiple  cell,  and  using  a  solution  of  copper  sul- 
phate in  0.0125  normal  sulphuric  acid  as  electrolyte.  As  table  15  shows, 
no  constant  results  could  be  obtained. 

At  first  the  potentials  were  all  higher  than  the  theoretical  and  later  they 
all  became  lower.  Evidently  the  copper  reacts  with  the  electrolyte,  form- 
ing cuprous  salt,  and  this  reaction  proceeded  further  in  proportion  in  the 
case  of  the  more  concentrated  amalgam,  because  of  its  lesser  volume  and 
larger  proportion  of  exposed  surface.42  Another  series  of  readings  was 
then  tried,  with  additional  precautions.  The  original  amalgam  was, 
in  this  case,  made  by  standing  amalgamated  copper  wire  in  mercury,  in  an 
atmosphere  of  hydrogen,  for  several  days — the  mercury  being  frequently 
shaken.  It  was  drawn  into  the  pipettes  in  the  usual  way,  wholly  out  of 
contact  with  the  air.  The  electrolyte,  again  slightly  acid,  was  also  allowed 
to  stand  in  an  atmosphere  of  hydrogen  over  a  copper  amalgam  for  several 
days.  In  spite  of  these  precautions  no  more  constant  results  were  obtained, 
as  table  16  shows. 

TABLE  16. 


Cell. 

Electromotive  force,  in  millivolts. 

Observed. 

Theoretical. 

As  soon  as 
possible. 

i  hour. 

6  hours. 

24  hours. 

48  hours. 

1-2 
1-3 
1-4 

10.  60 
26.2 
29-5 

ii.  9 
28.5 
29.6 

^'3 
26.7 

29.9 

II.  I 
21.9 
24-5 

6.4 

IO.I 
12.5 

9.58 
21.91 

30.66 

Evidently  the  electrolyte  was  not  saturated  with  cuprous  salt,  in  spite 
of  its  week's  contact  with  the  amalgam.  Considering  the  small  concentra- 
tion in  the  amalgam  and  the  fact  that  it  can  act  upon  the  electrolyte  only 
at  the  surface  in  mercury,  this  is  perhaps  not  surprising. 

In  the  light  of  these  experiments,  let  us  turn  back  for  a  moment  to  the 
results  of  Meyer  and  Spencer.  The  latter's  are  wholly  comprehensible. 
His  first  cell  alone  was  dilute  enough  to  be  beyond  the  limit  of  saturation, 
and  that  gave  a  result  like  ours.  The  other  more  concentrated  amalgams 
must  have  contained  traces  of  solid,  and  if  he  had  waited  until  they  reached 
equilibrium,  his  cell  III  must  have  reached  zero  potential.  His  figures  are 
just  what  one  would  have  expected. 

Meyer's  figures  are  harder  to  explain.  How  he  could  have  attained  his 
results  from  amalgams  containing  a  large  excess  of  solid  phase  will 


"See   for  example,  Richards,  Collins,  and  Heimrod,   Proc.  Am.  Acad.,  35,   125 
(1899);  Zeit.  phys.  Chem.,  32,  324  (1900). 


54  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

always  remain  a  mystery.  Perhaps  the  compensating  effects  of  rate  of 
solution  and  degree  of  saturation  may  have  combined  to  give  the  results 
he  observed,  or  perhaps  his  potentials  came  not  from  copper  at  all,  but 
rather  from  some  impurity. 

It  would  have  been  particularly  interesting  to  have  obtained  good 
results  in  the  case  of  this  amalgam,  for  the  electrolytic  solution  pressure 
of  copper  is  of  the  same  order  of  magnitude  as  that  of  mercury,  and  it 
might  be  expected  that  a  balanced  action  would  be  established  between 
the  passage  of  mercury  into  the  electrolyte  and  of  copper  into  the  amal- 
gam. This  idea,  which  has  been  followed  up  by  Hulett  and  De  Lury  in 
another  way  since  the  beginning  of  our  work,  was  one  of  the  secondary 
objects  of  the  present  research.  A  balanced  action,  indeed,  may  be  in 
part  the  cause  of  the  lack  of  constancy  of  the  potentials  observed,  as  one 
would  be  led  to  expect  from  this  cause  a  gradual  fall  in  potential.  It  is 
possible  that  if  the  electrolyte  were  wholly  saturated  with  cuprous  sul- 
phate, satisfactory  measurements  might  be  obtained,  and  one  of  us  hopes 
to  return  to  the  problem  in  the  future. 

IRON  AMALGAM. 

J.  P.  Joule  "  seems  to  have  been  the  first  person  to  study  iron  amalgams. 
He  records  that  an  amalgam  containing  I  per  cent  of  iron  is  fluid,  and  3 
per  cent  is  semi-fluid. 

An  amalgam  containing  I  per  cent  of  iron  was  therefore  made,  by  elec- 
trolysis. This  amalgam  on  filtration  through  soft  leather  proved  to  be  a 
suspension.  The  amalgam  was  filtered  twice  more,  and  finally  the  mercury 
in  a  weighed  amount  of  the  amalgam  was  evaporated,  and  the  remaining 
ferric  oxide  was  weighed.  The  same  process  was  repeated  with  a  fresh 
amalgam  similarly  prepared.  In  the  first  instance,  65.0  grams  of  amalgam 
gave  0.0013  gram  of  Fe2O4;  solubility  0.00135  per  cent.  In  the  second, 
143.0  grams  gave  0.0027  grams  of  Fe2Os ;  solubility  0.00133  per  cent 

Thus  the  solubility  of  iron  in  mercury  can  not  greatly  exceed  I  milli- 
gram in  i oo  grams.  There  is  no  proof  that  even  this  small  trace  might 
not  have  percolated  in  the  solid  state  through  the  leather.  As  the  solu- 
bility is  so  small,  the  investigation  of  the  potential  of  iron  amalgams  was 
not  pursued  further. 

a  Journ.  Chem.  Soc.,  16,  378  (1863). 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM  55 

LITHIUM  AMALGAMS. 

Up  to  the  beginning  of  last  year  but  little  accurate  work  had  been  done 
on  the  amalgams  of  the  alkali-metals  from  the  standpoint  of  potential 
measurements.  The  very  recent  discovery  by  Lewis  and  Kraus  of  a 
satisfactory  method  of  measuring  these  metals  against  an  aqueous  solution 
of  their  hydroxides  was  not  known  to  us  at  the  time  of  our  work,  hence 
its  assistance  was  not  available.4*  The  first  step  in  the  present  quest  was 
obviously  a  repetition  of  the  earlier  work  in  the  hope  of  discovering  its 
validity.  If  this  promised  well,  more  accurate  determinations  were  to  be 
attempted. 

Meyer  and  Cady,  in  their  publications  already  cited,  have  furnished  the 
chief  figures  concerning  the  electrochemistry  of  the  amalgams  of  the 
alkali-metals.  Meyer  recorded  the  results  on  sodium  amalgam,  but,  as 
he  spoke  of  using  an  aqueous  electrolyte  apparently  without  suitable  pre- 
cautions, his  data  have  little  significance.  Cady,  working  under  Bancroft's 
direction,  made  measurements  upon  amalgams  of  the  three  most  plentiful 
alkali-metals,  using  pyridine  as  the  solvent  for  the  electrolyte.  This  work 
shows  the  effects  of  great  haste ;  the  figures  in  his  tables  are  not  wholly 
consistent  with  themselves  and  are  evidently  vitiated  by  serious  errors, 
both  of  experiment  and  of  proof-reading.  Therefore  it  was  thought 
advisable  to  repeat  his  work.  We  employed  at  first  as  the  electrolyte  a 
solution  of  lithium  chloride  in  pyridine.  The  specimen  of  salt  employed 
was  a  very  pure  sample  which  was  being  used  for  work  on  atomic  weights 
in  this  laboratory.  We  are  greatly  indebted  to  Mr.  H.  H.  Willard  for  his 
kindness  in  providing  it.  As  a  solvent  the  best  pyridine,  supplied  by  Kahl- 
baum,  was  redistilled  with  a  fractionating  column,  giving  as  boiling-point 
H5.2°±o.i°  at  760°  mm.  It  was  always  protected  from  moisture  during 
distillation,  and  was  subsequently  kept  in  a  potash  desiccator.  The  con- 
ductivity of  lithium  chloride  "  in  pyridine  is  very  small,  hence  the  electro- 
lyte was  made  very  nearly  saturated. 

The  amalgams  were  made  by  placing  mercury  and  lithium  in  the  lower 
of  the  two  bulbs  in  the  usual  apparatus  shown  in  fig.  I,  page  9,  sealing 
everything  into  its  place,  and  finally  melting  the  lithium  after  the  whole 
apparatus  had  been  filled  with  hydrogen.  After  cooling,  the  amalgam  was 
driven  by  the  pressure  of  hydrogen  into  the  upper  pipette,  from  which  a 
sample  was  taken  for  alkalimetric  analysis  by  means  of  digestion  with  a 
standard  acid  solution.  Two  amalgams  made  in  this  way,  which  were 
expected  to  give  concentrations  of  about  o.i  and  0.5  per  cent,  were  found 
to  contain  0.037  Per  cen^  an<^  °-°36  per  cent  respectively ;  and  in  both 

"This  method  has  not  yet  been  published.  In  the  near  future  it  will  be  applied 
either  by  Lewis  and  Kraus  or  at  the  Harvard  Laboratory  to  a  series  of  measure- 
ments like  those  discussed  in  the  present  paper. 

aLasezynski  and  Gorski,  Zeitschr.  f.  Electrochem.,  4,  290. 


56  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

cases  solid  amalgams  could  be  seen  floating  on  the  liquid  amalgam  in  the 
pipettes.  Hence  it  was  evident  that  the  solubility  of  lithium  in  mercury  is 
about  0.036  per  cent.  This  agrees  well  with  the  observation  of  Kerp  and 
Bottger,46  who  obtained  a  solid  amalgam  containing  0.69  per  cent  to  0.72 
per  cent  (having  approximately  the  formula  LiHgg)  from  a  mother-liquor 
containing  0.04  per  cent  of  lithium.  In  view  of  these  facts  it  is  evident 
that  Cady  was  much  in  error  in  his  supposition  that  his  amalgam  contained 
1.8  per  cent  of  lithium — far  more  than  corresponds  even  to  the  solid 
amalgam.  In  answer  to  our  personal  enquiry,  Professor  Cady  states  that 
the  cause  of  this  error  was  a  defective  method  of  analysis,  which  multiplied 
by  50  the  absolute  amount  of  lithium  in  each  amalgam,  but  did  not  affect 
the  ratio  of  the  two  concentrations. 

The  saturated  liquid  amalgam,  whose  preparation  is  described  above, 
we  diluted  to  form  two  less  concentrated  amalgams,  and  these  were  driven 
into  the  pipettes  under  hydrogen  in  the  usual  manner.  Analysis  showed 
them  to  contain  0.0255  Per  cent  an<3  0.0144  per  cent  of  lithium  respectively. 
With  these  amalgams  a  cell  was  set  up,  two  cups  being  filled  with  each. 
No  constant  readings  could  be  obtained,  but  the  value  0.0169  with  a  pos- 
sible error  of  0.0002  volt  was  indicated.  The  electromotive  force  deduced 
from  the  simple  concentration  law  equation  is  0.0159;  hence  it  appears 
that,  as  had  been  expected,  lithium  ranks  with  lead,  thallium,  and  indium 
rather  than  with  zinc  and  tin.  It  is  pleasant  to  note  that  this  result  agrees 
qualitatively  with  the  outcome  of  Cady's  experiments,  in  spite  of  their 
inconsistency  of  detail. 

The  cell  on  standing  rapidly  changed  in  potential,  and  in  a  few  hours  a 
number  of  small  crystals  were  observed  in  the  electrolyte,  which  itself 
had  assumed  a  dark-brown  color.  Hoping  to  establish  a  constant  con- 
dition in  a  fresh  portion  of  the  electrolyte,  in  order  to  obtain  better  results 
upon  refilling  the  cell,  we  allowed  the  solution  of  the  chloride  in  pyridine 
to  stand  over  metallic  lithium.  In  a  few  days  the  pyridine  had  become  of 
a  dark-blue  hue,  which  upon  opening  the  bottle  disappeared  in  a  very  few 
moments.  In  a  similar  bottle  containing  pyridine  and  lithium,  but  no 
lithium  chloride,  no  blue  color  was  formed,  but  nevertheless  the  lithium 
attacked  the  solvent  in  another  way,  and  a  brown  powder  was  deposited. 
It  thus  appears  that  dry  lithium  attacks  dry  pyridine,  and  the  hope  of 
obtaining  really  satisfactory  results  in  this  way  was  dispelled. 

Several  other  series  of  potential  measurements  were  tried,  in  some  of 
which  lithium  sulphate  took  the  place  of  the  chloride  in  the  electrolyte; 
but  the  series  recorded  above  was  the  most  satisfactory.  More  dilute 
amalgams  gave  more  erratic  potentials.  In  some  cases  a  potential  of  over 
one  volt  was  observed  for  several  minutes,  in  the  case  of  a  cell  where 
about  0.02  volt  was  the  value  which  theoretical  considerations  would  give. 

"Ze.it  anorg.  Chem.,  25,  i  (1900). 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM  57 

In  view  of  these  highly  unsatisfactory  results,  and  the  rapidly  approach- 
ing conclusion  of  the  academic  year,  it  was  decided  to  abandon  for  the 
present  the  attempt  to  obtain  accurate  data  concerning  the  alkali-metals, 
and  confine  the  theoretical  treatment  to  the  six  metals  which  had  given 
unimpeachable  results,  namely,  cadmium,  zinc,  thallium,  indium,  tin,  and 
lead.  The  theoretical  discussion  of  these  more  satisfactory  data  follows. 

APPLICATION  OF  THE  EQUATION  OF  CADY. 

It  has  already  been  pointed  out  in  the  preceding  paper"  that  if  the 
electromotive  force  of  a  cell  as  depicted  by  the  equation  of  Helmholtz  is 
made  equal  to  that  demanded  by  the  equation  of  Cady,  the  term  involving 
the  heat  of  reaction  is  eliminated,  and  we  obtain  the  expression  : 


This  equation  was  found  as  a  matter  of  fact  to  hold  approximately  true 
as  regards  thallium,  indium,  and  tin,  and  it  becomes  a  matter  of  interest 
as  applied  also  to  zinc  and  lead.  The  average  values  for  the  zinc  cells 

Mi-M3and  Ni-N3  are  given  on  p.  45.    The  value  of  £»  was  ^^  =9-15 

Cn  O.OQQo 

Thus 


3? 

Difference  =  0.000020 

This  small  difference,  not  much  exceeding  2  per  cent,  seems  at  first 
sight  inconsistent  with  the  wide  discrepancy  found  by  the  earlier  investi- 
gation as  regards  cells  containing  zinc  amalgams.  There  are  two  causes 
for  this  difference  of  verdict:  the  first  and  most  important  is  not  a  real 
inconsistency,  but  appears  only  because  of  the  different  mode  of  presenta- 
tion ;  the  second  subordinate  cause  of  difference  is  due  to  the  doubtful 
character  of  the  result  for  the  heat  of  dilution  previously  employed  —  a 
datum  wholly  eliminated  from  the  present  calculation.  This  latter  circum- 
stance will  be  considered  in  the  subsequent  heading  concerning  the  equa- 
tion of  Helmholtz  ;  the  former  is  worthy  of  a  further  word  of  explanation 
here. 

In  the  paper  by  Richards  and  Forbes,  the  equation  of  Cady  was  trans- 
posed thus  : 

RT       d        U 


This  monograph,  p.  31. 


58  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

and  the  two  members  were  calculated  separately  and  compared.  Thus 
all  the  errors,  both  of  theory  and  observation,  were  heaped  upon  the 

smallest  term  involved  f^K-l  and  naturally  formed  a  much  larger  per- 
centage of  this  smallest  term  than  they  would  when  applied,  as  in  the 

present  paper,  to  the  much  larger  term  —  =-  in  -£-  .     Cady's  equation  thus 

vr         Ci 

failed  as  applied  to  the  calculation  by  difference  of  the  smallest  term  ;  but 
the  present  method  of  presentation  shows  that  the  equation  may  be  of 
use  in  calculating  approximately  the  temperature  coefficient  of  an  amalgam 
cell.  I 

As  the  amalgams  become  more  dilute,  the  fulfilment  of  the  equation  of 
course  becomes  more  exact,  because  the  concentration  ratio  gives  more 
and  more  nearly  an  exact  measure  of  the  osmotic  work,  and  all  the  other 
irregularities  probably  decrease.  Thus  for  the  cell  M3-M4  (or  N3-N4), 
(pages  45  and  46),  where  ^  =  0.01395  volt,  An-  for  29.96°  =0.001541  volt, 
and  the  ratio  of  the  concentrations  is  3.305:  I,  the  following  results  are 
calculated  : 

Temperature  coefficient  calculated  from  concentrations..     0.0000515 
Actually  observed  temperature  coefficient  ...............     0.0000514 

The  difference  is  only  0.2  per  cent,  an  amount  distinctly  less  than  the 
experimental  error. 

Similar  calculations  for  lead  give  similar  results  ;  for  example,  let  us 
take  the  cell  Pi-P2,  having  a  concentration  ratio  equal  to  2.53.  Then 


Difference  =  0.0000008 

In  the  more  dilute  cell  Qi-Q2  where  the  concentration  ratio  =  6.21,  we 
have 

Temperature  coefficient  calculated  from  concentrations  =  0.0000786 
Temperature  coefficient  actually  observed  .............  =  0.0000793 

With  this  more  dilute  amalgam  the  difference  is  less  than  i  per  cent 
instead  of  being  2  per  cent  as  in  the  case  of  the  more  concentrated  lead 
cell. 

Turning  back,  now,  to  cadmium,  investigated  by  Richards  and  Forbes, 
we  find  that  the  results  recorded  there  give  somewhat  similar  indications, 
when  compared  according  to  the  present  method.  Thus  the  cell  1-5  ** 
(made  from  an  amalgam  containing  2.955  Per  cen^  of  cadmium  and 
another  amalgam  obtained  by  diluting  12.226  grams  of  this  amalgam  with 

**  Carnegie  Institution  of  Washington  Publication  No.  56,  46  (1906). 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,   AND   LITHIUM 


59 


12.762  grams  of  mercury)  gave  a  potential  of  0.009405  volt  at  23.03°,  and 
must  have  had  a  value  for  the  function  ^^,=0.003655.*' 
From  these  facts  the  following  results  may  be  calculated : 
£.,-&_  8.316 


,0.703. 


=0.0000303 


£f  =  0.003655^0  =  0.003655  TM°  -23      .    ....=0.0000318 


Difference  ..............................  =0.0000015 

Thus  the  discrepancy,  which  (according  to  the  previous  method  of  cal- 
culation, already  explained  in  the  case  of  zinc)  had  seemed  very  large 
when  heaped  upon  the  smallest  term,  does  not  exceed  5  per  cent  when 
applied  to  the  larger  terms. 

Thus  all  the  six  metals,  thallium,  indium,  tin,  lead,  zinc,  and  cadmium, 
show  an  approximate  agreement  with  the  Cady  equation,  when  tested  in 
this  way.  The  discrepancy  never  exceeds  5  per  cent,  and  usually  is  little 
greater  than  2  per  cent.  The  deviations  are  sometimes  in  one  direction, 
and  sometimes  in  another,  and  in  some  cases  are  no  greater  than  the  errors 
of  experimentation.  For  the  sake  of  convenient  reference,  it  is  worth 
while  to  present  in  a  single  table  all  these  results  concerning  the  equation 


Although  by  no  means  giving  all  the  results  which  may  be  calculated 
from  the  measurements,  table  17  presents  a  typical  example  of  each  metal, 
as  well  as  of  the  effect  of  increasing  dilution. 

TABLE  ij.—The  Application  of  the  Equation  Derived  from  that  of  Cady. 


Designation 

Per  cent  of 
solid  metal  in 

Temperatur 

e  coefficient. 

of  cell. 

concentrated 
amalgams. 

Observed. 

Calculated. 

Thallium  

Cl-C2 

1.84 

O.OOOI08 

O.OOOIO8 

Do  

B2-B3 

o.  172 

o  000104 

o  000106 

Indium 

Ei-E2 

1  .92 

o  000044 

o  000046 

Tin 

Ji-T2 

O.2I 

o  000052 

o  000053 

Zinc 

Mi-M3 

o  91 

o  000093 

o  000095 

Do 

M3-M4 

O   IO 

o  000051 

o  000051 

Lead 

Pl-P2 

I   O2 

o  000073 

o  000075 

Do 

Qi-Q2 

0   IO 

o  000079 

0.000079 

R  &  F  1-5 

2  Q5 

o  000032 

0.000030 

The  theoretical  significance  of  the  close  agreements  shown  in  this  table 
is  worth  further  attention. 


40  Carnegie  Institution  of  Washington,  Publication  No.  56,  p.  50. 


6o 


ELECTROCHEMICAL   INVESTIGATION    OF   LIQUID   AMALGAMS 


The  outcome  may  be  stated  as  follows :  The  temperature  coefficient  of 
the  electromotive  force  of  a  cell  made  from  liquid  amalgams  is  as  a  matter 
of  fact  approximately  equal  to  the  ideal  potential  of  the  cell  (calculated 
from  the  relative  concentrations  of  the  amalgams)  divided  by  the  absolute 
temperature.  The  result  is  independent  of  the  temperature:  the  increase 
of  potential  is  a  linear  function.  This  has  already  been  shown  experi- 
mentally.50 

One  may  well  inquire  concerning1  the  ultimate  significance  of  this 
phenomenon ;  and  the  following  suggestion  is  offered  as  a  tentative 
explanation. 

In  these  cells,  the  change  of  heat  capacity  during  the  reaction  is  very 
small.  Hence  according  to  the  theorem  recently  advanced  by  one  of  the 
present  authors,51  the  free  energy  output  of  the  chemical  part  of  the  change 
may  be  expected  to  be  equal  to  the  total  energy  output,  and  both  would 
be  expected  to  remain  invariable  with  the  temperature.  Thus  the  part  of 
the  electromotive  force  due  to  the  chemical  change  would  have  no  tem- 
perature coefficient,  and  all  the  change  of  potential  with  temperature  must 
be  ascribed  to  the  change  in  the  osmotic  work.  This  would  be  expected 
to  be  linear,  and  directly  dependent  upon  the  concentrations  as  it  is  actually 
found  to  be,  at  least  approximately.  The  rule  would  be  expected  to  hold 
only  when  no  change  of  heat  capacity  occurs  in  the  reaction.  Thus  these 
troublesome  and  time-consuming  measurements  have  shed  new  light  upon 
the  mechanism  of  the  galvanic  cell,  and  have  justified  the  labor  expended 
upon  them. 

TABLE  18. — Calculation  of  E.  M.  F.,  by  Cady's  Equation. 


Metals. 

Designation 
of  cell. 

Observed 
potential 
atO°. 

Potential 

according  to 
Cady* 

Difference, 
error  of  Cady 
equation. 

Error  of 
simple 
concentration 
equation. 

Thallium.   . 

Cl-C2 

Yolt. 

o  03390 

Volt. 
O  01102 

Millivolt. 

+0  02 

—  4  41 

Do 

C2-C3 

o  02048 

o  02060 

+O   12 

—  I   O2 

Indium  
Tin  

Ei-E2 

Jl-J2 

0.01445 
o  01361 

0.01493 

o  01415 

+0.48 
-hO    54 

-1.86 

+0   QO 

Zinc  

Mi-M2 

o  02424 

o  02477 

+  0   *S\ 

+  1  28 

Cadmium  
Lead.     .     . 

R&Fi-s 

PI-P2 

0.00867* 

o  00896 

0.00830* 
o  00914 

-0.37 
_l_o  18 

-0.34 

-hi   0^ 

Do 

P2-P4 

o  01626 

o  01663 

+O  17 

+o  68 

Do 

Qi-Ql 

o  03138 

o  0112^ 

—  0   IS 

+o  24 

These  are  reduced  to  o°  from  the  observations  at  23°. 


'*  This  conclusion  may  be  drawn  from  the  table  on  p.  22. 

81  Richards,  Proc.  Am.  Acad.,  36,  300  (1002);  Zeitschr,  phys.  Chem.,  42,  138 
(1902).  This  theorem  has  been  elaborated  by  Nernst  in  a  very  interesting  way. 
(See  Nernst's  Silliman  Lectures.)  "Thermodynamics  and  Chemistry,"  page  56, 
New  York,  1907. 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM 


6 1 


The  equation  of  Cady  may  also  be  used  to  calculate  the  electromotive 
force  from  the  heat  of  reaction  and  the  concentration  effect,  supposing 
these  to  be  known.  Indeed,  this  corresponds  to  Cady's  first  method  of 
expressing  the  results.  In  a  subsequent  section  the  heats  of  reaction  are 
calculated  with  the  help  of  the  temperature  coefficient  and  the  equation 
of  Helmholtz.  Using  the  values  for  U  there  given  and  the  values  of  the 
concentration  ratios  already  presented  in  this  section,  the  given  results 
in  table  18  are  obtained  from  the  Cady  equation 


On  comparing  these  results  in  the  fifth  column  with  those  in  the  sixth, 
it  is  evident  that  Cady's  equation  is  a  much  closer  approximation  to  the 
truth  than  von  Turin's.  The  average  deviation  shown  by  Cady's  equation 
is  only  about  0.3  millivolt,  whereas  the  average  deviation  shown  by  the 
simpler  equation  is  about  1.3  millivolt.  In  other  words  the  departure  of 
the  potential  from  the  simple  values  indicated  by  the  gas  law  may  be 
ascribed  chiefly  to  the  heat  of  reaction.  Clearly,  however,  the  differences, 
although  much  smaller  than  before,  are  still  probably  in  most  cases  beyond 
the  limit  of  error  of  the  experimentation.  It  will  be  noticed  that  in  the 
case  of  the  concentrated  thallium  cell  the  Cady  equation  is  almost  exactly 
right  ;  in  the  cases  of  tin,  zinc,  and  the  concentrated  lead  cells  the  correc- 
tion afforded  by  the  heat  of  reaction  is  not  enough  to  explain  the  deviation 
from  the  simple  concentration  law  ;  in  the  cases  of  the  indium  cells  and  the 
dilute  thallium  and  lead  cells,  the  heat  of  dilution  supplies  too  large  a  cor- 
rection, and  in  the  case  of  cadmium  the  correction  is  in  the  wrong 
direction. 

It  is  interesting  to  observe  that,  assuming  U  to  be  constant  at  different 
temperatures,  Cady's  equation  predicts  that  the  difference  between  the 
observed  values  and  those  calculated  from  the  concentrations  alone  by 
the  simpler  equation  should  be  independent  of  the  temperature  also.  By 
reference  to  the  tables  this  will  be  seen  to  be  the  case  with  considerable 
approximation  with  all  the  metals  concerned  in  these  tables. 

The  figures  for  thallium  and  lead  (table  19),  taken  from  foregoing 
tables  2  and  u,  may  serve  as  examples: 

TABLE  19.  —  Difference  between  Observed   Values  and  Concentration   Values, 
in  Millivolts. 


Tempera- 
ture. 
(°C.). 

Cell 

Cl-C2. 

Cell 
C*-C3. 

Cell 
C3-C4. 

Cell 

Pl-P2. 

Cell 
Pa-P4. 

Cell 
Q«-Q3. 

0 

4.364 

1.  014 
0080 

0.266 

o  263 

1-935 

0.983 

0.258 

30 

4-357 

1.  000 

0.266 

1-957 

1.022 

0.242 

62  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

This  approximate  constancy  of  the  value  of  TT  obs.  —  TT  calc.  at  different 
temperatures  had  already  been  observed  by  Cady,62  and  was  recognized  by 
him  as  proving  the  heat  of  dilution  of  the  cell  was  constant  over  the  range 
of  temperature  used.  His  confirmation  was  far  less  exact  than  ours, 
however.  The  relation  is  not  only  of  theoretical  interest,  but  is  also 
useful  practically,  as  it  offers  a  means  of  checking  the  potentiometer 
measurements. 

The  deviations  from  the  exact  fulfilment  of  Cady's  equation  must  be 
ascribed,  as  they  were  in  the  previous  paper,  to  the  inexactness  of  the 

expression  In  — ,  as  a  means  of  estimating  the  free  energy  of  the  osmotic 

C-L 

effect.  As  was  said  before,  these  irregularities  can  hardly  be  traced  with 
exactness  until  precise  measurements  of  the  osmotic  pressures  of  the  amal- 
gams have  been  made;  and  such  are  not  yet  available.  The  paper  of 
Richards  and  Forbes,  already  so  often  quoted,  amplifies  the  obvious  fact 
that  the  formation  of  hydrargyrates  in  solution  will  tend  to  increase  the 
observed  potential,  while  the  polymerization  of  the  dissolved  metal  will 
tend  to  diminish  it.  This  paper  disclosed  also  the  fact  that  if  in  the  case 
of  cadmium  allowance  is  made  for  the  space  occupied  by  the  dissolved 
cadmium,  a  large  part  of  the  difference  between  the  theoretical  and 
observed  values  is  eliminated.  According  to  a  previously  made  similar 
observation  of  Morse  and  Frazer,58  the  excessive  osmotic  pressure  of 
sugar  solutions  is  to  be  corrected  in  a  similar  way. 

Very  recently  Lewis  "  has  pointed  out  in  an  interesting  paper  that  a 
more  generally  accurate  method  of  expressing  osmotic  effect  is  found  in 
the  generalization  expressed  essentially  as  follows :  "  The  activity  of  a 
substance  is  proportional  to  its  mol-fraction."  Thus  instead  of  expressing 
the  electrically  manifested  osmotic  effect  of  a  concentration  cell  by  the 

equation  it—  ^~  In  —  one  may  express  it  as  TT=  ^~  In  — — —  /  — - — -= 
vb        c<i  vr       n  +  NI  I  n  +  NI 

where  n  signifies  the  numbers  of  gram-molecules  of  dissolved  substance 
and  Nl  and  N2  those  of  the  solvent  in  the  two  amalgams  respectively. 
This  is  essentially  an  application  of  the  equation  of  Raoult  to  electro- 
motive force.  On  the  same  pattern  the  equation  of  Cady  would  become 

x_    U   ,  RT lan  +  N* 
vF  *  VF  '*  +  & 

Neither  of  these  equations  is  given  in  just  this  form  by  Lewis  in  his 
paper,  but  each  is  an  immediate  outcome  of  his  reasoning. 

MJourn.  Phys.  Chem.,  2,  page  562. 

58  Am.  Chem.  J.,  34,  i  (1905)  ;  37,  324,  425,  558;  38,  175  (1907). 

MG.  N.  Lewis;  J.  Am.  Chem.  Soc.,  30,  668  (1908).  See  also  Lewis,  Zeit.  phys. 
Chem.,  61,  163  (1907).  In  connection  with  this  latter  article,  read  Journ.  phys. 
Chem.,  4,  389  (1900). 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM 


It  is  easy  to  see  that  neither  of  these  equations  will  give  very  different 
results  from  the  concentration-equations  in  the  present  cases.  Indeed,  if 
the  atomic  volume  of  the  substance  in  solution  is  the  same  as  that  of 
mercury,  the  two  roads  lead  to  exactly  the  same  numerical  goal,  as  is 
seen  from  the  following  logic. 

It  is  obvious  that  in  general  N  —  ^——,  where  N  equals  the  number 

M     A 

of  gram-molecules,  W  the  total  weight  of  substance,  V  the  total  volume  of 
substance  and  M  and  A  the  atomic  weight  and  atomic  volume,  respectively. 
Using  capital  letters  to  denote  the  solvent  and  small  letters  to  denote  the 
dissolved  substance,  we  have  the  following  expression : 


if  a  is  taken  to  mean  the  atomic  volume  of  the  dissolved  substance  in  its 
dissolved  state,  that  is  to  say,  the  increased  volume  which  a  gram-atom 
causes  in  the  mercury,  and  v  the  similar  volume  of  the  amount  of  the 
substance  under  consideration.  In  this  equation  when  A  —  a  both  cancel, 
and  the  last  member  of  the  equation  takes  a  form  identical  with  the 
preceding  and  gives  like  results,  but  with  V  and  v  in  place  of  N  and  n. 
This  consequence  might  not  be  perceived  at  first  sight  from  Lewis's  paper. 
On  the  other  hand,  when  A~>a,  the  Raoult  law  will  give  a  lower  theo- 
retical value  than  the  concentration  law;  and  when  A<a,  the  opposite  is 
true.  The  metals  concerned  at  present  have  so  nearly  the  same  atomic 
volumes  that  the  deviations  are  very  slight,  as  is  shown  in  the  following 
table  (all  the  cells  were  at  o°C.)  : 

TABLE  20. — Comparison  of  Raoulfs  Equation  with  Concentration  Equation. 


Metals. 

Cell. 

*At.  volume 
of  dissolved 
metal. 

Comparison  of 
at.  volume. 

Calculated  by 
Raoult 
equation. 

Calculated  by 
concentration 
equation. 

Thallium  
Indium  

CI-C2 

Ei-E2 

I7.6 
15.5 

A<a 
A<a 

Millivolts. 
29-59 
12.  60 

Millivolts. 
29-53 
12.59 

Cadmium  
Pure  mercury.  .  . 

R&Fi-s 

II.  9 
14.8 

A>a 

8.28 

8.33 

*  These  values  are  calculated  from  the  densities  of  amalgams  on  page  13. 

On  comparing  the  last  two  columns,  the  differences  are  seen  to  be 
small,  and  with  more  dilute  amalgams  they  are  yet  smaller. 

It  will  be  observed  that  in  cases  of  this  kind  both  of  these  equations 
give  results  very  different  indeed  from  the  mode  of  calculation  which 


64  ELECTROCHEMICAL   INVESTIGATION   OF  LIQUID   AMALGAMS 

takes  account  only  of  the  space  occupied  by  the  solvent,  where 
7r=^r  In  — .  The  latter  method  will  evidently,  as  has  been  found  by 

Richards  and  Forbes,  give  a  much  higher  value.  For  the  cadmium  cell 
this  was  found  to  be  8.56  millivolts  at  o°  C,  instead  of  about  8.3  given  by 
the  equations  above,  the  actually  observed  value  being  8.67  at  o°.55 

In  any  case,  it  is  clear  that  the  new  method  of  calculating  the  results 
from  the  equation  of  Raoult  throws  no  light  upon  the  major  deviations 
of  the  cells  from  the  equation  of  Cady,  for  these  deviations  are  far  too 
great  to  be  explained  by  such  insignificant  alterations  in  the  numbers 
predicted  by  theory,  and  some  of  the  changes  are  in  the  wrong  direction. 
On  this  account,  it  was  thought  unnecessary  to  recalculate  the  new  theo- 
retical values  for  each  case. 

As  an  outcome  of  these  considerations,  one  may  say  that  while  the 
equation  of  Cady  in  one  or  other  of  its  forms  affords  a  fairly  satisfactory 
means  of  calculating  the  temperature  coefficient  of  an  amalgam  cell  (and 
probably  also  of  other  cells  in  which  there  is  but  little  change  of  heat 
capacity),  and  the  best  available  means  of  finding  the  potential  without 
electrical  measurement,  it  does  not  afford  a  good  method  of  determining 
the  heat  of  dilution.  This  latter  quantity  is  to  be  much  more  accurately 
found  with  the  help  of  the  equation  of  Helmholtz,  to  which  the  reader's 
attention  is  now  directed. 

EQUATION  OF  HELMHOLTZ. 

In  the  first  part  of  this  monograph  the  temperature  coefficients  of  the 
cells  consisting  of  amalgams  of  thallium,  indium,  and  tin  were  used  for 
computing  the  heat  of  dilution,  according  to  the  equation  of  Helmholtz. 
The  same  calculation  may  now  be  applied  to  zinc,  cadmium,  and  lead. 
Turning  first  to  the  case  of  zinc,  we  may  take  the  cell  Mi-M3  where 
TTO  =  24.237  millivolts  and  ATT  between  o°  and  29.96°  €.  =  2.799  millivolts." 
Because  the  temperature  coefficient  has  been  shown  to  be  very  nearly  if  not 
quite  independent  of  the  temperature,  the  value  given  may  be  used  at  o°. 
Then 

*»vp    4679.2  joules 

ATT 

vFT~£/p 4926.0  joules 

U     -246.8  joules 

This  value  for  the  heat  of  dilution,  —246.8  joules,  or  —59.0  calories, 
is  considerably  greater  than  the  value  —52  joules  found  by  actual  ther- 
mochemical  experiments.  The  difference  is  due  in  part  to  the  fact  that 

"Richards  and  Forbes,  Carnegie  Institution  of  Washington,   Publication  56,  p. 
62  (1906).    The  values  there  given  are  for  23°. 
*  This  paper,  p.  45. 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM  65 

the  cell  in  the  present  calculation  involved  much  further  dilution  than 
that  corresponding  to  the  thermochemical  experiment.  In  the  present 
case  one  amalgam  was  about  nine  times  as  dilute  as  the  other,  while  in  the 
thermochemical  experiment  the  dilution  was  only  to  double  the  bulk. 
Nevertheless,  even  allowing  for  the  heat  which  would  be  absorbed  by  the 
further  dilution  of  the  amalgams,  it  is  clear  that  the  electrochemical 
estimate  of  the  cooling  effect  exceeds  the  actual  thermochemical  measure- 
ment. This  lack  of  coincidence  was  to  have  been  expected  from  the 
results  already  chronicled  in  the  preceding  section  of  the  monograph, 
concerning  thallium,  indium,  and  tin  ;  in  each  of  these  cases  also  the  ther- 
mochemical effect  appeared  to  be  too  small,  and  in  the  case  of  lead,  soon 
to  be  discussed,  the  same  discrepancy  was  observed.  The  lack  of  agree- 
ment is  undoubtedly  due  not  to  fault  in  the  Helmholtz  equation,  but 
rather  to  the  inadequacy  of  the  clockwork  stirrer  used  in  the  thermo- 
chemical work.  Liquid  amalgams,  because  of  their  great  inertia,  are  hard 
to  mix  ;  but  their  ready  conductivity  quickly  establishes  a  nearly  equable 
temperature  throughout,  even  when  they  are  not  thoroughly  mixed. 
Hence  it  is  easy  to  be  deceived  concerning  the  results. 

In  spite  of  the  lack  of  exact  agreement,  the  thermochemical  result  of 
Richards  and  Forbes  is  nevertheless  of  value,  for  it  shows  that  liquid  zinc 
amalgams  really  produce  a  large  cooling  effect  upon  dilution,  and  it  thus 
confirms,  both  as  to  sign  and  as  to  order  of  magnitude,  the  results  of  the 
electrical  measurements. 

Turning  to  cadmium  we  find  that  the  work  of  Richards  and  Forbes  has 
quantitative  as  well  as  qualitative  significance.  By  reference  to  the  origi- 

nal data,"  it  is  seen  that  at  o°  ^=30.826  millivolts  and  —  ~  =0.003655, 

TT0U  j( 

therefore 

•fvp    ......................................       5951  joules 

S9S7  J°ules 


—6  joules 


This  difference  is  no  larger  than  the  possible  error  of  experiment,  and  its 
sign  is  therefore  somewhat  uncertain  ;  but  nevertheless  it  is  supported  by 
the  very  small  cooling  effect  which  was  at  that  time  actually  found.  In 
this  case,  the  inadequacy  of  the  mixing  in  the  thermochemical  experiment 
would  have  very  little  significance,  because  the  effect  to  be  observed 
formed  so  trifling  a  part  of  the  whole  phenomenon. 

In  this  connection  it  may  be  noted  that  Carhart  "*  assumes  on  the  basis 
of  his  theory,  without  any  published  experimental  justification,  that  the 

"Carnegie  Institution  of  Washington,  Publication  No.  56,  pp.  50  and  57  (1906). 
"Phys.  Rev.,  26,  p.  216  (1908). 


66  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

heat  of  dilution  of  cadmium  amalgams  is  positive,  not  negative.  In  our 
experience,  this  assumption  is  contrary  to  fact.  With  the  help  of  Dr.  H. 
L.  Frevert  one  of  us  has  found  that  solid  cadmium  amalgams  produce  a 
large  cooling  effect  on  dissolving  in  more  mercury,  and  there  is  every 
reason  to  believe  that  the  dilution  of  liquid  cadmium  amalgams  is  like- 
wise an  endothermic  reaction,  although  its  thermal  effect  is  so  small  as  to 
make  accurate  measurement  difficult.  The  dilution  of  a  3  per  cent 
cadmium  amalgam  with  an  equal  bulk  of  mercury  would  evolve  over  30 
joules  of  heat  if  Car  hart's  theory  were  correct,  and  this  would  have  raised 
the  temperature  of  the  calorimetric  system  by  0.02°.  So  large  a  thermal 
effect  could  not  have  escaped  detection. 

This  example  remains  the  most  precise  verification  of  the  Helmholtz 
equation  which  has  ever  been  offered,  coming  within  the  experimental 
error  of  about  o.  I  per  cent.  The  interesting  measurements  of  Carhart " 
show  an  average  deviation  of  nearly  2  per  cent. 

Turning  now  to  lead,  we  find  results  very  like  those  of  zinc  and  tin. 
Let  us  take  the  cell  Pi-P2,  of  which  TTO  =  0.008960  and  ATT  for  29.96°  C. 
=0.001175.  Then 

r»vF    1730  joules 

ATT 
vFT  2^-= 2068  joules 

U    -  338  joules 

The  attempt  was  made  to  verify  this  value  by  actual  thermochemical 
experiment,  using  the  same  apparatus  as  in  the  other  cases  already  men- 
tioned in  the  previous  papers.  The  apparatus  was  not  suited  for  exact 
quantitative  work,  but  the  test  was  enough  to  show  a  very  decided  cooling 
effect  (of  0.018°  C.)  in  the  apparatus,  and  to  confirm  in  sign  and  in  order 
of  magnitude  the  figure  calculated  from  the  electrical  measurements. 

Calculated  in  the  same  way  from  the  electrical  measurements  of  the 
other  lead  cells,  the  values  for  the  heat  of  dilution  are  found  to  decrease 
as  the  dilution  increases.  Figures  for  three  lead  cells  are  given  in  table 
21  to  serve  as  typical  examples  of  this  phenomenon,  which  of  course 
appears  in  the  measurements  with  other  metals  also,  in  so  far  as  their 
degrees  of  accuracy  permit.  It  is  interesting  to  note  that  the  maximum 
cooling  effect  of  dilution  has  not  been  wholly  reached  in  a  solution  contain- 
ing only  o.i  per  cent  of  lead  (or  I  gram-atom  in  15  liters)  ;  for  an  amal- 
gam of  this  considerable  dilution  is  still  found  to  absorb  20  calories  more 
upon  dilution  to  fourteen  times  its  volume.  This  last  exceedingly  attenu- 
ated material  would  probably  absorb  very  little  more  on  further  dilution ; 
hence  the  limiting  value  is  probably  not  far  off.  According  to  these  results, 

"Carhart,  Phys.  Rev.,  March,  1908. 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM 


67 


then,  a  gram-atom  of  lead  dissolved  in  a  hundred  gram-atoms  of  mercury 
must  absorb  about  540  joules  or  130  calories  on  infinite  dilution;  and  of 
this  amount  about  two-thirds  is  absorbed  when  the  amalgam  is  diluted 
with  twice  its  bulk  of  mercury. 

With  these  figures  are  repeated  also,  in  conveniently  accessible  form, 
the  other  results  obtained  in  this  monograph  by  the  application  of  the 
equation  of  Helmholtz. 

TABLE  21. — Heat  of  Dilution  of  Amalgams  Calculated  from  the  Electrical 
Measurements. 


Metal. 

Designation 
of  cell. 

Range  of  dilution 
(per  cent  of  metal). 

Heat  of  dilution  per  gram-atom 
of  solid  metal. 

Joules. 

Gram  calories. 

Thallium  

CI-C2 

C2-C3 
Ei-Ea 
Gi-Ga 
Ji-Ja 

MI-MS 

R  &  F  i-s 

PI-P2 
P2-P4 

Qi-Q3 

1.84  to  0.53 

0.53          0.23 
I.Q2          0.38 

0.016      0.008 
0.21        0.061 
0.91        o.io 
2.45        0.29 

1.02          0.40 
0.40          0.093 

o.io       0.007 

+427 
+  109 
+677 

^ 

I24? 
-338 
-117 

-  77 

+  102.3 
+   26.1 
+  161.9 
-      I. 
-    I6.5 

-  59-0 
-     1.4 
-  80.8 
-  28.0 
-  20.3 

Do  

Indium  
Do  
Tin 

Zinc 

Cadmium 

Lead  .  . 

Do 

Do  

Because  the  heat  capacity  of  the  reacting  system  is  essentially  constant, 
these  values  are  independent  of  the  temperature,  as  far  as  our  measure- 
ments were  concerned.  Their  chief  uncertainty  depends  upon  the  diffi- 
culty of  measuring  exactly  the  temperature  coefficients  of  small  electro- 
motive forces;  but  they  are  accurate  enough  to  serve  as  a  fairly  close 
guide  to  the  behavior  of  the  respective  amalgams.  They  are  hardly  close 
enough  to  serve  as  the  basis  for  a  search  after  an  exact  mathematical  law 
governing  the  change  of  thermal  effect  with  increasing  dilution,  although 
such  a  search  would  be  an  interesting  aspect  of  yet  more  precise  measure- 
ments. 


68  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

COMPARISON  OF  DEVIATIONS  FROM  CONCENTRATION  LAW. 

As  in  the  case  of  the  previous  paper,  it  is  interesting  to  compare  the 
deviations  of  the  potentials  given  by  various  amalgamated  metals  from 
the  requirement  of  the  simple  concentration  law.  In  order  to  make  the 
understanding  of  this  matter  more  vivid,  there  are  given  together  in  the 
following  diagram  the  several  curves  showing  the  deviations  of  the  various 
potentials  from  the  concentration  equation.  These  lines  are  all  drawn 
upon  the  same  scale  and  are  arranged  so  that  for  any  ordinate  the  atomic 
concentration  is  identical.  If  the  equation  of  Cady  represented  a  complete 
correction,  it  would  reduce  all  the  lines  to  the  horizontal  straight  line 
marked  O.  As  a  matter  of  fact  only  about  three-quarters  of  the  devia- 
tions, on  the  average,  are  to  be  explained  in  this  way  ;  and  only  thallium 
and  lead  are  brought  nearer  to  the  horizontal  line  than  the  unconnected 
curve  for  cadmium. 

These  curves,  therefore,  not  only  give  an  excellent  collective  picture  of 
the  behavior  of  these  amalgams,  but  they  enable  anyone  with  a  compara- 
tively small  expenditure  of  time  to  compute  the  potential  which  would 
actually  exist  between  two  amalgams  of  the  same  metal  between  these 
limits  of  concentration.  The  divisions  in  the  direction  of  abscissae  mean 
in  each  case  the  doubling  of  the  volume.  Suppose  one  wished  to  deter- 
mine the  potential  between  an  amalgam  of  a  given  concentration  and  that 
of  one-fourth  its  concentration.  The  place  of  the  more  concentrated 
amalgam  is  found  upon  the  proper  curve  and  the  second  one  will  be  just 
two  divisions  to  the  right.  The  difference  between  the  ordinates  corre- 
sponding to  these  two  points  will  give  the  deviation  from  the  exact  gas 
law  for  that  particular  combination.  Accordingly  the  potential  is  to  be 
computed  according  to  the  following  equation  : 


in  which  ATT  designates  the  difference  between  the  ordinates  just  men- 
tioned. If  any  dilution  other  than  2,  4,  8,  16  is  desired  the  appropriate 
point  may  easily  be  found  from  these  and  a  table  of  logarithms,  it  being 
borne  in  mind  that  each  large  division  in  the  direction  of  abscissae  signi- 
fies 0.30103  for  Briggs's  logarithms  or  0.6932  for  natural  logarithms.  The 
scale  of  the  curves  here  depicted  is  rather  small  for  an  accurate  determi- 
nation. Obviously  the  potential  could  hardly  be  found  more  nearly  than 
perhaps  within  the  fiftieth  of  a  millivolt,  because  the  large  divisions  in  the 
direction  of  ordinates  represent  millivolts  ;  but  this  same  principle  might 
be  employed  on  a  larger  scale  and  with  more  accurate  data  to  within  any 
degree  of  precision  desired. 

It  will  be  noticed  that  all  the  curves  approach  horizontality  as  the 
deviation  proceeds.    It  is  clear  that  long  before  infinite  dilution  is  reached 


OF   ZINC,    CADMIUM,    LEAD,    COPPER,    AND   LITHIUM 


the  values  will  accord,  within  a  limit  of  error  of  measurement,  with  either 
the  equation  of  von  Turin  or  of  Cady.  This  seemed  to  us  so  clear  that 
further  prolongation  of  the  curves  to  the  right  seemed  to  us  hardly  worth 


-3 


log 2       Iog4      log 8       log  16      log3Z     log 64-    loglZB    Iog256   Iog5l2     log  1024 
Fig.  12.  The  Approach  of  the  Potentials  of  all  the  Amalgams  to  the  Concentration  Law. 

Deviations,  both  positive  and  negative,  are  plotted  in  millivolts  as  ordinates; 
logarithms  of  concentration  ratios  are  plotted  as  abscissae.  Thallium, 
indium,  and  cadmium  give  potentials  greater  than  those  corresponding 

to   the   equation  it  =  — -£r  '»  ~^~ ',    zinc,    lead,    and  tin   give   potentials  less 


than  the  actual  valu 
sponds  to  4.00  gram 
extends  to  amalgam 
per  256  liters).  Th 
almost  if  not  quite 


and 
solu 


bl3e°at 


excepting 


s  thus  computed.  The  origin  of  abscissae  corre- 
toms  of  dissolved  metal  per  liter,  and  the  diagram 
1024  times  as  dilute  as  this  (i.  e.,  i  gram-atom 
dotted  lines  are  extrapolated.  The  curves  ar; 
ndependent  of  temperature,  at  least  between  o* 
n  the  case  of  tin,  which  is  only  very  slightly 


7O  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

the  labor  involved,  especially  as  the  chance  of  error  increases  greatly  as 
the  amalgams  become  more  dilute.  The  possible  appearance  of  a  balanced 
reaction  at  great  dilution  we  attempted  to  detect  by  using,  not  greater 
dilutions,  but  rather  metals  with  the  least  possible  solution-tensions.  The 
interesting  work  of  Hulett  and  De  Lury,  published  after  ours  was  com- 
pleted, supplements  our  work  by  carrying  the  curve  of  one  of  the  metals, 
cadmium,  much  further  to  the  right  than  we  have  done.  Neither  of  our 
curves  shows  any  certain  indication  of  the  balanced  reaction  for  which 
Hulett  and  De  Lury  were  independently  seeking,  although  several  of  the 
metals  are  distinctly  less  electropositive  than  cadmium. 

In  conclusion,  we  take  pleasure  in  expressing  our  obligation  to  the 
Carnegie  Institution,  of  Washington,  for  generous  pecuniary  assistance. 


ELECTROCHEMICAL   INVESTIGATION    OF   LIQUID   AMALGAMS  7! 

SUMMARY. 

The  results  obtained  in  the  foregoing  papers  may  be  summarized  as 
follows : 

(1)  The  electromotive  forces  of  various  cells,  containing  amalgams  of 
thallium,  indium,  tin,  zinc,  lead,  copper,  and  lithium,  have  been  measured 
at  o°  and  30°,  with  many  precautions  against  experimental  errors. 

(2)  The  temperature  coefficients  of  cells   containing  zinc  amalgams 
were  also  obtained  by  actually  opposing  cells  at  o°  against  cells  at  30°. 

(3)  It  is  shown  that  in  every  case  the  more  concentrated  amalgams 
deviate  by  appreciable  amounts   from  the  theoretical  values  calculated 
from  the  simple  concentration  law,  thallium  and  indium  resembling  cad- 
mium in  giving  potentials  higher  than  those  demanded  by  the  concentra- 
tion law ;  whereas  lead  and  tin  resemble  zinc  in  giving  potentials  lower 
than  those  demanded  by  the  concentration  law.     Thallium  showed  the 
greatest  positive  deviation,  and  tin  and  lead  the  greatest  negative  deviation. 

(4)  It  is  shown  further  that  on  the  average  about  three  quarters  of 
each  of  these  deviations  are  to  be  explained  by  the  heat  of  dilution  of  the 
amalgam,  according  to  the  equation  of  Cady. 

(5)  The  other  quarter  of  the  deviation,  not  explained  by  the  equation 
of  Cady,  must  be  ascribed  either  to  experimental  error  or  more  probably 
to  the  inexactness  of  the  concentration  law.    Such  inexactness  would  be 
caused  either  by  polymerization  or  by  the  formation  of  hydrargyrates, 
according  as  the  computed  potential  is  greater  or  less  respectively  than 
the  observed  potential. 

(6)  It  is  shown  that  the  equation  of  Cady  requires  that  the  temperature 
coefficient  of  a  cell  of  this  type  should  be  equal  to  the  total  concentration 
effect  divided  by  the  absolute  temperature,  and  should  be  independent  of 
the  temperature.    The  verification  of  these  conclusions  is  shown  to  hold 
approximately  in  all  the  cases  studied,  by  comparison  with  the  actual 
values.     This  fact  affords  a  simple  method  of  computing  with  moderate 
accuracy  the  temperature  coefficient  of  the  electromotive  force  of  cell  of 
this  type,  without  having  recourse  to  electrical  measurement. 

(7)  It  is  shown  that  the  equation  of  Cady  is  not  well  adapted  for  com- 
puting the  heat  of  dilution,  for  in  this  case  all  the  errors  and  deviations 
accumulate  upon  the  smallest  term  of  the  equation. 

(8)  The  heats  of  dilution  of  these  various  amalgams  are  computed 
with  the  help  of  the  equation  of  Helmholtz ;  and  it  is  shown,  as  was  to  be 
expected,  that  the  heat  of  dilution  decreases  very  rapidly  as  the  dilution 
progresses. 

(9)  The  difficulties  of  actual  thermochemical  measurement  of  the  heat 
of  dilution  of  amalgams  are  emphasized. 


72  ELECTROCHEMICAL   INVESTIGATION   OF   LIQUID   AMALGAMS 

(10)  It  was  found  impossible  to  obtain  satisfactory  results  with  an 
electrolyte  containing  tin  in  a  quadrivalent  condition,  either  as  stannic 
chloride  or  as  sodium  stannate.  In  this  connection  it  was  pointed  out 
that  Cady  must  have  had  a  two-phase  amalgam  in  his  tin  cell,  and  that  his 
results  with  tin  were  illusory. 

(n)  The  solubility  of  copper  in  mercury  was  found  to  be  only  0.0024 
per  cent,  and  of  iron  0.00134  per  cent  by  weight,  amounts  too  small  to 
give  satisfactory  electrochemical  results.  The  results  of  Meyer  upon 
copper  are  shown  to  be  without  significance,  because  he  imagined  that  he 
used  a  much. more  concentrated  solution,  which  must  have  been  a  mere 
suspension  of  copper  in  mercury. 

(12)  It  is  shown  that  since  lithium  is  only  soluble  to  the  extent  of 
0.036  per  cent  by  weight  in  mercury,  the  results  of  Cady  upon  lithium  are 
likewise  questionable;  but  more  dilute  solutions  of  lithium  are  shown 
to  behave  in  a  general  way  as  Cady's  equation  requires.    No  exact  deter- 
minations were  made,  because  of  the  difficulty  of  finding  a  suitable  electro- 
lyte. 

(13)  All  the  deviations  from  the  simple  concentration  law  were  found 
to  decrease  as  dilution  increases,  so  that  upon  reaching  a  concentration 
of  o.oi  gram-atom  per  liter  all  the  amalgams  investigated  behaved  prac- 
tically as  ideal  solutions. 

( 14)  The  density  of  pure  indium  at  20°  was  found  to  be  7.28. 

(15)  The  densities  of  various  liquid  amalgams  of  thallium,  indium,  tin, 
and  lead  were  determined. 


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